Gauss-Newton Iterative Method Research Articles

Convergence analysis of simplified Gauss–Newton iterative method under a heuristic rule

Convergence analysis of simplified Gauss–Newton iterative method under a heuristic rule

Distributed wide-field electromagnetic method for coal mining goaf detection in a complex urban environment: A case study in Jinan, China

Urban expansion has resulted in many proposed projects located over coal mining zones, which has highlighted the importance of detecting the spatial scope and water abundance of goafs before the commencement of construction work. Although electromagnetic (EM) methods have proven effective for goaf detection, their applications in intensely noisy and urbanized environments remain limited. To address this challenge, we evaluate an investigation of a coal mining goaf in Jinan, China, using the distributed wide-field EM (DWFEM) method. A third-order [Formula: see text] sequence pseudorandom signal with 39 survey frequencies is transmitted to achieve long-time data acquisition at each station. Unlike the controlled-source audio-frequency magnetotellurics method, the DWFEM records only the electric field [Formula: see text] component. The synthetic model tests and field data demonstrate the consistency of the [Formula: see text] apparent resistivity and the Cagniard resistivity in the far field. The long-time acquisition and 1C recording greatly improve data quality and exploration efficiency. We also use an all-angle resistivity calculation formula and an electrode layout method parallel to the wire source to obtain electrical connections in different directions. The DWFEM inversion results are obtained using the 1D Gauss-Newton iterative method under a plane-wave assumption. By interpolating the data from different measurement stations, we image resistivity depth profiles and obtain 3D subsurface electrical data for the subsurface from 0 to 1000 m. We interpret the obtained profiles with geologic and mining information, revealing two significant water-enriched goaf areas. Validation is performed using seismic data and drill cores. The results significantly enhance our understanding of the characteristics of the coal mine under our project and highlight the applicability of the DWFEM for detecting goafs in complex urban environments.

Transformer Network-Aided Relative Pose Estimation for Non-cooperative Spacecraft Using Vision Sensor

AbstractThe objective of the proposed work is to perform monocular vision-based relative 6-DOF pose estimation of the non-cooperative target spacecraft relative to the chaser satellite in rendezvous operations. In this work, the convolutional neural network (CNN) is replaced by the high-resolution transformer network to predict the feature points of the target satellite. The self-attention mechanism inside the transformer provides the advantage of overcoming the inadequacies of the translation equivariance, 2D neighborhood awareness, and long-range dependencies in CNN. First, the 3D model of the target satellite is reconstructed using the inverse direct linear transform (IDLT) method. Then, the pose estimation pipeline is developed with a learning-based image-processing subsystem and geometric optimization of the pose solver. The image-processing subsystem performs target localization using CNN-based architecture. Then, the key points detection network performs regression to predict 2D key points using the transformer-based network. Afterward, the predicted key points based on their confidence scores are projected onto the corresponding 3D points, and the pose value is computed using the efficient perspective-n-point method. The pose is refined using the non-linear iterative Gauss–Newton method. The proposed architecture is trained and tested on the spacecraft pose estimation dataset and it shows superior accuracy both in translation and rotation values. The architecture has shown robustness against the drastically changing clutter background and light conditions in the space images due to the self-attention mechanism. Moreover, this method consumes less computation resources by using fewer floating-point operations and trainable parameters with low input image resolution.

Dimensionless Analysis of the Spatial–Temporal Coupling Characteristics of the Surrounding Rock Temperature Field in High Geothermal Roadway Realized by Gauss–Newton Iteration Method

Understanding the time–space coupling characteristics of the surrounding rock temperature field in high geothermal roadways is essential for controlling heat damage in mines. However, current research primarily focuses on individually analyzing the temperature changes in the surrounding rock of roadways, either over time or space. Therefore, the Gauss–Newton iteration method is employed to model the coupling relationship between temperature, time, and space. The results demonstrate that the dual coupling function describing the temperature field of the surrounding rock in both time and space provides a more comprehensive characterization of the temperature variations. Over time, as ventilation duration increases, the fitting degree of the characteristic curve steadily rises, and the characteristic curve descends overall. In the spatial dimension, the fitting degree of the characteristic curve gradually decreases with the rise of the dimensionless radius, and the characteristic curve ascends overall. Additionally, as thermal conductivity increases, the fitting degree of the characteristic curve steadily rises.

A hybrid of iterative Gauss–Newton and one-dimensional convolutional neural network for high-resolution electrical impedance tomography

We developed a processing method using benefits of both iterative Gauss–Newton (IGN) and a one-dimensional convolutional neural network (1D-CNN) for high-resolution electrical impedance tomography. The proposed method logically combines conductivity images reconstructed by different methods. The accuracies of the mathematical IGN method, 1D-CNN method, and the proposed method were compared. Utilizing the ideal potential data obtained through simulations, along with the experimental potential data derived from cement samples, we reconstruct the conductivity distribution. When utilizing the simulation data, the IGN method produces larger errors in the reconstructed images as the size of the foreign object decreases. The proposed method reconstructs the position and size more accurately than the IGN and 1D-CNN methods. When utilizing the experimental data, 1D-CNN and proposed methods were more accurate in terms of the position and size than the IGN method.

A novel efficient estimator for three‐dimensional bearings‐only source localisation with unknown sensor altitude and systematic measurement errors

AbstractA novel two‐stage profile maximum likelihood estimator is proposed to estimate the source location and the systematic errors jointly, with the aim of addressing the problem of source localisation using angle‐only measurements from a single sensor with unknown sensor altitude and systematic measurement errors. The proposed two‐stage profile maximum likelihood estimator algorithm is capable of decoupling the azimuth and elevation angle measurements while transforming the original maximum likelihood optimisation problem into two sub‐problems, that is, two‐dimensional‐projected maximum likelihood estimator and relative altitude maximum likelihood estimator. In terms of the two‐dimensional‐projected maximum likelihood estimator, an algorithm combining pseudo‐linear estimating and Kalman filtering is proposed to generate an initial estimate. Subsequently, a Gauss–Newton iterative method is developed to estimate the two‐dimensional‐projected target location and the azimuth systematic error jointly. The relative height maximum likelihood estimator is initialised using a pseudo‐linear estimator. Next, a Gauss–Newton iterative algorithm is adopted to estimate the elevation systematic error and the relative height. As indicated by the result of the simulation studies, the proposed algorithm exhibits an estimation performance close to the Cramér–Rao lower bound with unknown sensor altitude and systematic measurement errors.

An Efficient Discretization Scheme for Solving Nonlinear Ill-Posed Problems

Abstract Information based complexity analysis in computing the solution of various practical problems is of great importance in recent years. The amount of discrete information required to compute the solution plays an important role in the computational complexity of the problem. Although this approach has been applied successfully for linear problems, no effort has been made in literature to apply it to nonlinear problems. This article addresses this problem by considering an efficient discretization scheme to discretize nonlinear ill-posed problems. We apply the discretization scheme in the context of a simplified Gauss–Newton iterative method and show that our scheme requires only less amount of information for computing the solution. The convergence analysis and error estimates are derived. Numerical examples are provided to illustrate the fact that the scheme can be implemented successfully. The theoretical and numerical study asserts that the scheme can be employed to nonlinear problems.

Sensing Method for Wet Spraying Process of Tunnel Wall Based on the Laser LiDAR in Complex Environment.

In tunnel lining construction, the traditional manual wet spraying operation is labor-intensive and can be challenging to ensure consistent quality. To address this, this study proposes a LiDAR-based method for sensing the thickness of tunnel wet spray, which aims to improve efficiency and quality. The proposed method utilizes an adaptive point cloud standardization processing algorithm to address differing point cloud postures and missing data, and the segmented Lamé curve is employed to fit the tunnel design axis using the Gauss-Newton iteration method. This establishes a mathematical model of the tunnel section and enables the analysis and perception of the thickness of the tunnel to be wet sprayed through comparison with the actual inner contour line and the design line of the tunnel. Experimental results show that the proposed method is effective in sensing the thickness of tunnel wet spray, with important implications for promoting intelligent wet spraying operations, improving wet spraying quality, and reducing labor costs in tunnel lining construction.

Research on UWB indoor 3D positioning algorithm based on the least squares method

With the increased use of rescue robots in indoor scenarios, the requirements for indoor location services are becoming more stringent. Traditional GPS positioning cannot provide accurate location information indoors, while ultra-wideband (UWB) has been widely used for indoor positioning due to its high accuracy and penetrating power. When solving 3D positioning coordinates using UWB least squares in line-of-sight situations, the positioning accuracy is easily affected by the layout height of the base station. In this paper, we first improve the positioning algorithm and then find a better way of base station layout in the actual positioning environment to improve the tag positioning accuracy. The algorithm improvement is based on the following ideas: firstly, the initial positioning results of the tag are obtained using UWB least squares and spatial geometric relations, and the 3D coordinates of the tag are solved using Gauss-Newton iterative method, and finally combined with the Kalman filter for optimization. The base stations are laid out in such a way that adjacent base stations are not at the same horizontal height and relative base stations are at the same horizontal height.

Intelligent Prediction Method for Heat Dissipation State of Converter Heatsink

Currently, the offline manual periodic detection method is a well-established practice in detecting the thermal state of the converter heatsink. This method, however, is huge in maintenance costs. To lower maintenance costs and improve maintenance efficiency in detecting the thermal dissipation state, this paper proposes an intelligent online prediction scheme based on Gauss-Newton iteration method. Firstly, the power loss model of the power module is established according to the characteristics of IGBT and FWD. The power loss of the power device is then calculated in real time with the voltage and current parameters of the converter. Next, the transient thermal model of the heatsink is established based on thermodynamics theory. And the calculation method of steady thermal resistance of heatsink based on Gauss-Newton iteration method is proposed according to the model. The transient thermal impedance data allow for timely prediction of thermal resistance of the heatsink and characterize the thermal state of the heatsink. Finally, with the help of DSP28377D, an experimental platform is built to verify the scheme. Results show that this method can realize intelligent prediction of thermal state online.

Interval Q factor estimation based on an improved frequency shift method

To characterize seismic attenuation information quantitatively, the qualify factor Q is routinely used in seismic exploration. To obtain a more reliable Q value than the peak frequency shift (PFS) method, the improved frequency shift (IFS) method computes the peak frequency by the centroid frequency (CF) to improve the noise immunity. However, the IFS method assumes all wavelets are the standard Ricker shape and ignores the effect of attenuation on the wavelet, which greatly affects the accuracy of estimated Q values, especially in interlayer computations. Some analytical methods try to replace the original hypothesis with attenuated Ricker wavelets, but there are too many mathematical approximations, resulting in inaccurate analytical results. Here, a new formula is derived by matching the spectrums with the attenuated Ricker wavelets. The peak frequencies (PFs) of the reference and attenuated wavelet are calculated by the Gauss-Newton iteration method. Combined with fitted PFs, we derive another new formula to calculate the interval-Q value directly. With these modifications, the PFS improved (PFSI) method not only improves the accuracy of the Q factor but also has noise robustness. The synthetic data tests and field data application demonstrate the feasibility and effectiveness of the proposed method.

Gauss–Newton iteration method for radial basis function-based postdistortions in visible light communication systems

In visible light communication systems, the inherent nonlinear characteristics of light-emitting diodes (LEDs) are the primary source of signal distortion. To alleviate the nonlinear effect of the LED and improve the system reliability, the polynomial method is used to construct the postdistorter. With strong processing ability and high solution accuracy, radial basis function (RBF) interpolation can also be used to alleviate the nonlinear effect. In terms of the iterative implementations, recursive least squares (RLS) algorithm has been widely adopted, but performance loss exists with the solution since RLS is initially proposed for linear regressions. Aiming at the nonlinear characteristics of post distortions, Gauss–Newton (GN) method is investigated to accomplish the iterations in this paper, where Taylor series expansion is used to approximate the nonlinear regression model. Simulation results show that the RBF can obtain better bit error ratio performance than polynomial, and the proposed GN iterations have significantly better performance compared to RLS in mitigating the nonlinear effect of LED.

Spatially constrained inversion of semi-airborne transient electromagnetic data based on a mixed norm

The interpretation of semi-airborne transient electromagnetic data is mainly based on a one-dimensional inversion algorithm. The continuity of the resistivity profile is generally poor when the data noise is strong because the resistivity is laterally unconstrained, and the constraint between the resistivity in the vertical distribution is usually taken as the L2 norm regular term. However, the main disadvantage of this regularization constraint is that it over-smoothens the model and cannot effectively describe the interface information of an abrupt electrical change. To address these issues, this paper proposes a mixed norm spatially constrained inversion (SCI) algorithm that adopts the L1 norm regularization term for the vertical spatial constraint and the L2 norm regularization term for the lateral spatial constraint. The Gauss-Newton iterative method is used to solve the objective function. Fixed and adaptive strategies are proposed for the regularization factors, and a parameter is used to adjust the weights of the two constraints. The influence of different constraint weights on the results is analyzed. The inversion of noisy synthetic data verifies that the proposed SCI algorithm has a higher resolution for electrical interfaces and better noise suppression effect than the L2 norm SCI algorithm. The inversion of field data shows a good effect and practicability.

Research on Quantitative Analysis of Multiple Factors Affecting COVID-19 Spread.

The Corona Virus Disease 2019 (COVID-19) is spreading all over the world. Quantitative analysis of the effects of various factors on the spread of the epidemic will help people better understand the transmission characteristics of SARS-CoV-2, thus providing a theoretical basis for governments to develop epidemic prevention and control strategies. This article uses public data sets from The Center for Systems Science and Engineering at Johns Hopkins University (JHU CSSE), Air Quality Open Data Platform, China Meteorological Data Network, and WorldPop website to construct experimental data. The epidemic situation is predicted by Dual-link BiGRU Network, and the relationship between epidemic spread and various feature factors is quantitatively analyzed by the Gauss-Newton iteration Method. The study found that population density has the greatest positive correlation to the spread of the epidemic among the selected feature factors, followed by the number of landing flights. The number of newly diagnosed daily will increase by 1.08% for every 1% of the population density, the number of newly diagnosed daily will increase by 0.98% for every 1% of the number of landing flights. The results of this study show that the control of social distance and population movement has a high priority in epidemic prevention and control strategies, and it can play a very important role in controlling the spread of the epidemic.

Optimisation Method for Determination of Crack Tip Position Based on Gauss-Newton Iterative Technique

In the digital image correlation research of fatigue crack growth rate, the accuracy of the crack tip position determines the accuracy of the calculation of the stress intensity factor, thereby affecting the life prediction. This paper proposes a Gauss-Newton iteration method for solving the crack tip position. The conventional linear fitting method provides an iterative initial solution for this method, and the preconditioned conjugate gradient method is used to solve the ill-conditioned matrix. A noise-added artificial displacement field is used to verify the feasibility of the method, which shows that all parameters can be solved with satisfactory results. The actual stress intensity factor solution case shows that the stress intensity factor value obtained by the method in this paper is very close to the finite element result, and the relative error between the two is only − 0.621%; The Williams coefficient obtained by this method can also better define the contour of the plastic zone at the crack tip, and the maximum relative error with the test plastic zone area is − 11.29%. The relative error between the contour of the plastic zone defined by the conventional method and the area of the experimental plastic zone reached a maximum of 26.05%. The crack tip coordinates, stress intensity factors, and plastic zone contour changes in the loading and unloading phases are explored. The results show that the crack tip change during the loading process is faster than the change during the unloading process; the stress intensity factor during the unloading process under the same load condition is larger than that during the loading process; under the same load, the theoretical plastic zone during the unloading process is higher than that during the loading process.

A novel estimator for the equation of state of the IGM by Ly α forest tomography

ABSTRACT We present a novel procedure to estimate the equation of state of the intergalactic medium in the quasi-linear regime of structure formation based on Ly α forest tomography and apply it to 21 high-quality quasar spectra from the UVES_SQUAD survey at redshift z = 2.5. Our estimation is based on a full tomographic inversion of the line of sight. We invert the data with two different inversion algorithms, the iterative Gauss–Newton method and the regularized probability conservation approach, which depend on different priors and compare the inversion results in flux space and in density space. In this way our method combines fitting of absorption profiles in flux space with an analysis of the recovered density distributions featuring prior knowledge of the matter distribution. Our estimates are more precise than existing estimates, in particular on small redshift bins. In particular, we model the temperature–density relation with a power law and observe for the temperature at mean density $T_0 = 13\,400^{+1700}_{-1300}\, \mathrm{K}$ and for the slope of the power law (polytropic index) γ = 1.42 ± 0.11 for the power-law parameters describing the temperature–density relation. Moreover, we measure an photoionization rate $\Gamma _{-12} = 1.1^{+0.16}_{-0.17}$. An implementation of the inversion techniques used will be made publicly available.

EUCALYPTUS GRANDIS X EUCALYPTUS UROPHYLLA GROWTH CURVE IN DIFFERENT SITE CLASSIFICATIONS, CONSIDERING RESIDUAL AUTOCORRELATION

Brazil is a major producer in the timber sector, mainly with the use of wood from species of the genus Eucalyptus, with 26.1% of planted forests located in Minas Gerais. Researchers and manufacturers have been searching for techniques with the objective of making full use of these forests, with a primary focus on greater growth. A modeling of growth curves is an alternative for the estimation of  oral production andan important aid tool for the researcher's decision making. Growth curves are commonly studied by nonlinear regression models, which have important assumptions that if not met should be added to the model. The present work aims to select among nonlinear Logistic, Gompertz and von Bertalany regression models the most suitable to describe the growth in wood volume of Eucalyptus urophylla x Eucalyptus grandis hybrids in three Forest Site categories, including whether assumption deviations are required. Methods were executed by the Gauss-Newton iterative method implemented in nls() and it gnls() functions of the R software. Determination coecient, Akaike information criterion (AICc) and Residual Standard Deviation (RSD) were used as selection evaluators of the best model. The results demonstrate that for all site categories, the Gompertz model with addition of autoregressive parameters AR (1) is the most appropriate to describe the growth in wood volume of Eucalyptus urophylla x Eucalyptus grandis hybrids. The addition of the rst-order autoregressive parameter does not aect the quality of t, but it is the correct procedure. Site I, which presents the largest trees according to pre-dened variations, recorded 308 m3/ha of wood volume, followed by 286 m3/ha and 263 m3/ha for Sites II and III, respectively. The time for Site III to reach the maximum point of volume growth is between the fourth and sixth year, while the other sites are more precocious, reaching this point between the second and third year.

A Novel Radial-Composite Model of Pressure Transient Analysis for Multistage Fracturing Horizontal Wells with Stimulated Reservoir Volume

In the process of stimulated reservoir volume of tight reservoir, horizontal well can form three zones, the inner zone is multistage fracturing zone, the middle zone is skin damage zone, and the outer zone is undamaged zone. In this paper, a transient well test analysis model of multistage fracturing horizontal well in three area composite reservoir is proposed. Based on Laplace transformation, point source integration, and superposition principle, the infinite conductivity multifracture model of three area composite reservoir is obtained. The linear equations of finite conductivity multifracture in Laplace space are established by using the equal conditions of flow and pressure at the fracture wall. Gauss-Newton iteration method and Stehfest number are used to obtain the solution of wellbore pressure. The accuracy of the results is verified by numerical simulation. Then, the flow characteristics of multistage fracturing horizontal wells in three area composite reservoirs are analyzed by type curves. The flow is divided into ten stages, which are the bilinear flow, the linear flow, the first radial flow stage, the inner zone linear flow, the inner zone radial flow, the middle zone linear flow, the middle zone radial flow, the outer zone linear flow, the outer zone radial flow, and the boundary dominated flow. The pressure derivative curves show different characteristics in different flow stages. The influences of fracture conductivity, fracture spacing, radius ratio of the middle zone to inner zone, radius ratio of the outer zone to the middle zone, permeability ratio of inner zone to the middle zone, permeability ratio of inner zone to outer zone, storage capacity ratio of inner zone to the middle zone, and storage capacity ratio of inner zone to outer zone on type curves are analyzed. Finally, the application and reliability of the proposed model are verified by a case example.

Numerical Method for the Solution of Algebraic Fuzzy Complex Equations

In this paper, the numerical solution of an algebraic complex fuzzy equation of degree ${n}$, based on the parametric fuzzy numbers, is discussed. The unknown variable and right-hand side of the equation are considered as fuzzy complex numbers, whereas, the coefficients of the equation, are considered to be real crisp numbers. The given method is a numerical method and proposed based on the separation of the real and imaginary parts of the equation and using the parametric forms of the fuzzy numbers in the form of polynomials of degree at most ${m}$. In this case, a system of nonlinear equations achieved. To get the solutions of the system, we used the Gauss-Newton iterative method. We also very briefly explain the conjugate of the solution of such equations. Finally, the efficiency and quality of the given method are tested by applying it to some numerical examples.

A GIT algorithm for simultaneous estimation of seismic source, site response and regional-distance dependent attenuation parameters: application to synthetic and real data

The generalized inversion technique (GIT) of earthquake recordings is a useful tool in retrieving seismic source spectra, attenuation path parameters and site transfer functions (TF). Further understanding of these three fundamental factors which control seismic ground motion constitutes one of the main challenges in seismology. Especially, the site TF estimation is an important objective that can significantly contribute to seismic hazard assessment. In this study, a parametric GIT algorithm (in MATLAB (The MathWorks, Inc., Natick, Massachusetts, United States, 2017)), based on the one proposed by Drouet et al. (Bull Seism Soc Am 98:198–219, 2008a), is developed, by introducing distance- and regional-dependent attenuation parameters for geometrical spreading and anelastic attenuation terms, respectively. This step is aimed at a more detailed investigation of attenuation path, anticipating to improve the knowledge of all three fundamental factors controlling seismic ground motion. The algorithm is based on a Gauss-Newton iterative inversion method, using initial reasonable model parameters. Source term is parametrically investigated for seismic moment and corner frequency, which can be simultaneously controlled with respect to stress drop. A synthetic dataset, approximating a simplified real dataset was inverted by the proposed inversion algorithm examining its computational validity. Four tests were implemented, with or without reference condition, providing encouraging results. The applicability of the algorithm is supported by the inversion of a real dataset which was also examined by Grendas et al. (Bull Earthq Eng 16:5061–5094, 2018) using a uniform attenuation model in GIT. Approximately 9% reduction of the misfit between real and computed data from the inverted model data is achieved, showing the effectiveness of the proposed algorithm.