Gauss-Newton Research Articles

Two-dimensional magnetotelluric inversion using unstructured triangular mesh implemented in Julia

This study presents a 2-D magnetotelluric inversion code tailored for unstructured triangular meshes, developed using Julia, a high-level, high-performance programming language designed for scientific and numerical computation. The forward modeling engine utilizes a node-based finite element method to solve electromagnetic fields throughout the modeling domain. The inversion process employs the Gauss-Newton optimization algorithm, iteratively updating the model via the minimization of a regularized least-squares objective function. We verified the accuracy of the forward modeling using two reference models and performed a synthetic inversion experiment to validate our inversion method and stress the necessity of accurately handling topography-influenced data. Through its application to constructing an electrical resistivity model beneath the northwestern end of Sumatra Island, Indonesia, we demonstrate the practicality of our code for inverting field datasets.

A Gauss–Newton method for mixed least squares-total least squares problems

A Gauss–Newton method for mixed least squares-total least squares problems

Characterization of complex stiffness and thickness of isotropic, viscoelastic plates using multi-modal Lamb waves

This paper presents an approach exploiting the sensitivity of Lamb waves for characterizing the mechanical and geometrical properties of plates. The analytical sensitivity functions are first derived in the case of an isotropic plate and are integrated into an iterative inverse problem to optimize its mechanical and geometrical properties based on a zero-finding approach (Gauss-Newton algorithm for a multivariable problem). This method is validated numerically for a viscoelastic plate and shows high accuracy and low computational cost when compared to existing methods. The design af an experimental setup based on dedicated air-coupled transducers is proposed by optimizing the shape and size of the transducers in order to increase sensitivity of the measred signals with respect to the mechanical parameters of the structure of insterest. Experimental validation demonstrates the ability of the methodto assess simultaneously the viscoelastic properties and the thickness of isotropic plate-like structures.

Computer vision-based real-time deflection monitoring of complex and sizeable steel structures

Deflection, as an intuitive index, plays a pivotal role in assessing the load-bearing capability and structural integrity of complex and sizable steel structures. Notwithstanding, the conventional contact measurement is limited to static deflection and necessitates work stands and manual readings. Therefore, it hinders the attainment of dynamic deflection and fails to cater to the engineering demands of real-time and prolonged monitoring. By leveraging the advancements in computer vision technology, we propose an innovative system for real-time deflection monitoring of complex and sizable steel structures, particularly suitable for monotonic deformation induced by prolonged loading. Specifically, the off-axis-based displacement measurement method was adopted to surmount the constraint of requiring the optical axis of the camera to be perpendicular to the target. Additionally, the inverse compositional Gauss-Newton (IC-GN) algorithm and parallel computation based on seed point diffusion were exploited to boost the matching and computing efficiency for attaining real-time monitoring of multi-points. To validate the efficacy of the proposed system, we conducted static load monitoring tests on a Bailey beam, with a height of 29.5 m and length of 16.5 m per span, as part of the Alibaba Jiangsu headquarters project in Nanjing. The collected test data were compared with the results from a laser displacement sensor and the ABAQUS model. The outcomes substantiate that the system is capable of non-contact, expeditious, and straightforward installation, besides achieving high accuracy and real-time deflection monitoring. This system serves as a sophisticated solution for health monitoring in constructing complex and sizeable steel structures and further contributes to realizing construction intelligence.

Research on image deformation monitoring algorithm based on binocular vision

Monitoring the deformation of critical structures such as tunnel、buildings and bridges is critical to ensure the safety of infrastructures. Non-contact deformation monitoring technology based on digital imagery has emerged as a prevalent and effective monitoring method, which enables cost-effective and efficient tracking of structural deformations. This paper aims to develop an automated deformation monitoring methodology using the binocular vision. First, standard preprocessing of digital images is performed through the integration of filtering algorithms and image enhancement techniques. Furthermore, by combining the Scale Invariant Feature Transform (SIFT) feature matching algorithm, the inverse compositional gauss–newton iterative algorithm, and interpolation methodologies, the planar displacement of the monitored targets can be calculated precisely, with sub-pixel precision being achieved. Subsequently, by adopting an enhanced Semi-Global Matching (SGM) algorithm, stereo matching of binocular images were accomplished. This process yields a disparity map, from which the depth map is computed. Then, precise measurement of the vertical displacement of the monitoring target can be obtained. This enables accurate measurement of three-dimensional displacements of the monitored targets. Finally, the developed methodology undergoes a comparative assessment against traditional measurement methods and existing algorithms to validate its measurement accuracy. The results prove that the deformation measurement technique based on binocular vision proposed in this paper captures structural deformation effectively. The accuracy surpasses that of existing measurement algorithms, and its efficiency outperforms traditional measurement methods.

Evaluation of susceptibility of Amaranthus species to the herbicide trifloxysulfuron-sodium using nonlinear models

Various elements have the potential to negatively impact crops in the agricultural sector, such as the presence of weeds that compete for essential resources, hindering growth and production and resulting in financial losses. There are several methods employed for weed control, among which herbicides stand out for requiring less labor and lower costs compared to others, especially in large-scale cultivation. The objective of this study was to use nonlinear models to assess the dose-response curve of the herbicide trifloxysulfuron-sodium applied to weeds of the genus Amaranthus. Data were collected at doses of 16D, 4D, D, 1/4D, 1/16D, 1/64D, and absence of products, where (D) represents doses of 7.5 and 17.5 The models were adjusted using the least squares method, employing the Gauss-Newton algorithm in the R software. Quality evaluation criteria included the coefficient of determination, residual standard deviation, Akaike information criterion, and the Bates and Watts curvatures. The fitted models met the assumptions of normality, independence of residuals, and homogeneous variance. Based on the results, the Michaelis Menten model was considered the most suitable for describing the data. It was observed that Amaranthus species exhibit variations in susceptibility to the herbicide, with A. hybridus and A. deflexus being the least and most susceptible, respectively, requiring doses of 6.02 and 306.90 to achieve 95% control.

Hygroscopic behavior of noni leaf powder (Morinda citrifolia L.) obtained by drying in foam layer

Studies on the ethnicbotanical aspect and properties of noni (Morinda citrifolia L.) reveal that noni leaves contain chemical compounds that are related to antibacterial, antioxidant, antiviral, antifungal, antitumor, anthelmintic, analgesic, inflammatory, hypotensive and immunostimulating, among these compounds are, for example, flavanoid glycosides. The drying process is, in turn, used as a way of preserving perishable products, such as plants, due to the removal of water available for microbial deterioration, keeping the properties of the material preserved. For proper storage and increasing the shelf life of the powder obtained after the drying process, it is important to know the adsorption isotherms. This study aims to survey the adsorption isotherms of powders obtained from noni leaves. The powders to be analyzed were obtained through the foam layer drying process in the maximum, minimum and central factorials of the complete experimental planning of previously carried out studies. For the mathematical adjustment of the obtained isotherms, three different mathematical models from the literature were tested, based on experimental moisture adsorption data, for non-linear regression analysis, using the Gauss-Newton and Levenberg-Marquardt methods. The isosteric heat of the powders was also calculated to understand the behavior of the adsorbed phase with temperature variation, in addition to the affinity between adsorbate and adsorbent. The noni leaf powder showed high hygroscopicity, ranging from 0.098 to 0.969 and the Oswin model was the one that best represented empirical adjustments describing the process. The isotherms were classified as Brunauer Type III. It was also possible to infer that the energy required to remove water present in the noni leaf powder decreases with increasing equilibrium humidity.

Rocket landing guidance based on second-order Picard-Chebyshev-Newton type algorithm

This paper proposes a rocket substage vertical landing guidance method based on the second-order Picard-Chebyshev-Newton type algorithm. Firstly, the continuous-time dynamic equation is discretized based on the natural second-order Picard iteration formulation and the Chebyshev polynomial. Secondly, the landing problem that considers terminal constraints is transformed into a nonlinear least-squares problem with respect to the terminal constraint function and solved with the Gauss-Newton method. In addition, the projection method is introduced to the iteration process of the Gauss-Newton method to realize the inequality constraints of the thrust. Finally, the closed-loop strategy for rocket substage vertical landing guidance is proposed and the numerical simulations of the rocket vertical landing stage are carried out. The simulation results demonstrate that compared with the sequential convex optimization algorithm, the proposed algorithm has higher computational efficiency.

An analytic approach for the moment-of-fluid interface reconstruction method on tetrahedral meshes

This article presents an original fast and robust approach for solving the moment-of-fluid interface reconstruction problem on tetrahedral meshes. We establish an explicit parametrization of the locus of the centroids under volume constrains using the spherical coordinates on a reference tetrahedron. This parametrization allows to write the moment-of-fluid objective function and its gradient by means of analytic formulas. Then, we show that the minimization problem on arbitrary tetrahedra can be effectively solved on the reference tetrahedron by using an affine transformation. Based on this transformation, we propose a improved technique for obtaining an initial condition for the minimization algorithm. We then describe the Gauss-Newton and the BFGS minimization algorithms, both combined with a trust-region method, to solve this reconstruction problem. Finally, we perform a verification and validation process on a series of increasingly complex test cases. These tests show that the proposed analytic method, paired with the Gauss-Newton algorithm, outperforms the other methods that were tested.

Simultaneous inversion of permeability, skin and boundary from pressure transient test data in three-dimensional single well reservoir model

This study presents a novel approach for simultaneous inversion of the key reservoir parameters like horizontal permeability, vertical permeability, skin, and boundary distances for spatial distribution across the grid cells in a 3D single well reservoir model (SWRM). These parameters are first estimated from the standard pressure transient analysis of well test pressure and rate data, which also act as a priori for the inverse problem. A field-worthy layer cake geological model is prepared based on the prior information obtained from pressure transient analysis, followed by a sequential flow simulation of field well test operation. The simulation results provide the model pressure versus rate data as the synthetic data for this study. A cost function is defined incorporating the well test pressure data and model pressure data, which would determine the convergence. The inversion process is to optimize the spatial distribution of reservoir parameters to minimize the difference between the measured pressure transient data and the modelled one, which is obtained from the multiphase fluid flow simulator that solves the implicit black-oil fluid-flow diffusivity equations at every step. A Gauss-Newton (GN) inversion scheme is used for the inversion. The reliability of inversion results depends on the accuracy of priori reservoir parameters fed to the solver, which can be refined if required through uncertainty parameter optimization (UPO). This approach helps to obtain a faster and reliable update of reservoir parameters in a layer cake homogeneous geomodel, hereby introducing the required heterogeneity. This increases the confidence and reliability of a geomodel, which is further used for various production prediction strategies.

Crescimento da linhaça oleaginosa descrito por modelo não linear logístico

ABSTRACT Knowledge on plant-atmosphere interactions is essential to understand the growth and development of agricultural crops. Thus, fitting growth curves is an important methodology to model plant growth and phenological stages. The study aimed to describe the growth of four oilseed flax materials cultivated in six agricultural years and with different sowing dates through the nonlinear logistic model. Nine experiments were carried out in Curitibanos, SC, Brazil, between 2014 and 2020, considering different sowing dates. Throughout the crop cycle, the number of leaves, number of secondary stems, plant height and total dry mass were measured. Nonlinear logistic model was fitted to the data, with the growth variables as the dependent variables and the accumulated thermal sum as the independent variable. Model fit and parameter estimation were obtained by ordinary least method, using a Gauss-Newton algorithm. The goodness of fit was measured by intrinsic and parametric nonlinearity, adjusted coefficient of determination, random standard error, standard deviation of fit, Akaike information criterion, and Bayesian information criterion. The performance of the nonlinear logistic model differed between the varieties and cultivars studied, in different years and sowing times. However, the use of the nonlinear logistic model improves inferences about the growth of oilseed flax, and the estimates of its parameters and critical points allow a biological and practical interpretation to assist in crop planning. Furthermore, the study suggests that the oilseed flax cycle is directly related to genotype × environment interactions, and when sown at later times, the materials tend to shorten their cycle.

An Inexact Sequential Quadratic Programming Method for Learning and Control of Recurrent Neural Networks.

This article considers the two-stage approach to solving a partially observable Markov decision process (POMDP): the identification stage and the (optimal) control stage. We present an inexact sequential quadratic programming framework for recurrent neural network learning (iSQPRL) for solving the identification stage of the POMDP, in which the true system is approximated by a recurrent neural network (RNN) with dynamically consistent overshooting (DCRNN). We formulate the learning problem as a constrained optimization problem and study the quadratic programming (QP) subproblem with a convergence analysis under a restarted Krylov-subspace iterative scheme that implicitly exploits the structure of the associated Karush-Kuhn-Tucker (KKT) subsystem. In the control stage, where a feedforward neural network (FNN) controller is designed on top of the RNN model, we adapt a generalized Gauss-Newton (GGN) algorithm that exploits useful approximations to the curvature terms of the training data and selects its mini-batch step size using a known property of some regularization function. Simulation results are provided to demonstrate the effectiveness of our approach.

Artificial Neural Network analysis on the effect of mixed convection in triangular-shaped geometry using water-based Al2O3 nanofluid.

The objective of the study is to investigate the fluid flow and heat transfer characteristics applying Artificial Neural Networks (ANN) analysis in triangular-shaped cavities for the analysis of magnetohydrodynamics (MHD) mixed convection with varying fluid velocity of water/Al2O3 nanofluid. No study has yet been conducted on this geometric configuration incorporating ANN analysis. Therefore, this study analyzes and predicts the complex interactions among fluid flow, heat transfer, and various influencing factors using ANN analysis. The process of finite element analysis was conducted, and the obtained results have been verified by previous literature. The Levenberg-Marquardt backpropagation technique was selected for ANN. Various values of the Richardson number (0.01 ≤ Ri ≤ 5), Hartmann number (0 ≤ Ha ≤ 100), Reynolds number (50 ≤ Re ≤ 200), and solid volume fraction of the nanofluid (ϕ = 1%, 3% and 4%) have been selected. The ANN model incorporates the Gauss-Newton method and the method of damped least squares, making it suitable for tackling complex problems with a high degree of non-linearity and uncertainty. The findings have been shown through the use of streamlines, isotherm plots, Nusselt numbers, and the estimated Nusselt number obtained by ANN. Increasing the solid volume fraction improves the rate of heat transmission for all situations with varying values of Ri, Re, and Ha. The Nusselt number is greater with larger values of the Ri and Re parameters, but it lessens for higher value of Ha. Furthermore, ANN demonstrates exceptional precision, as evidenced by the Mean Squared Error and R values of 1.05200e-6 and 0.999988, respectively.

Attenuation Tomography Using Low-frequency Ultrasound with Variational Autoencoder for Thorax Imaging: Experimental Study.

In this paper, we introduce a novel inversion methodology employing the variational autoencoder (VAE) for human thorax attenuation tomography using low-frequency ultrasound. The VAE is trained to assimilate the structural priors of the human thorax, utilizing training samples generated from computed tomography (CT) scans. This approach enables the compression of high-dimensional attenuation distributions into a lowerdimensional latent space. During the inversion process, the latent code is optimized, and then the reconstructed model is generated by the decoder of the VAE. This process can effectively integrate prior information of the domain of interest (DOI) into the inversion through coding and decoding, which would mitigate the ill-posedness of the inverse problem and facilitate better outcomes. Our method demonstrates robust generalization capabilities and noise resilience in numerical simulations, outperforming the conventional pixel-based Gauss-Newton method. Human subject experiment further corroborates the effectiveness of our approach. This is also the first experimental validation of the feasibility of low-frequency ultrasound functional imaging of the human thorax. Although the current study presents certain limitations, it underscores the potential of low-frequency ultrasound in the continuous monitoring of the human respiratory system.

Investigating the Growth of Bacteria using Double Sigmoid Model with Reparameterization

The growth of an organism can be modeled using a growth curve. However, bacteria's growth pattern differs from other organisms. Bacterial growth is divided into four phases: lag, logarithmic, stationary, and death. The experts re-parameterized the growth curve to match the growth phase of the bacteria. Bacterial growth patterns generally do not show a single sigmoid pattern but form two curves. Therefore, the double sigmoid model is more suitable. This study modeled the growth of the Pseudomonas putida bacteria by observing the optical density of the medium. Model parameters are estimated using the Non-Linear Least Square (NLS) method with the Gauss-Newton algorithm. The modeling results show that the double sigmoid model fits the growth curve of Pseudomonas putida better than the single sigmoid model. The Double Logistic model outperforms all models with the highest adjusted R2 and the smallest RMSE, AIC, and BIC values.

Gauss-Newton inversion with node-based basis functions: Application to imaging of seabed minerals in an area with rough bathymetry

The Gauss-Newton method has good convergence properties when used for the solution of seismic and electromagnetic inversion problems. One main issue is the high numerical cost. The numerical cost can be reduced if the optimization domain can be decoupled from the simulation domain such that the number of optimization parameters is much smaller than the number of grid nodes required for accurate simulation results. Overparameterization can be avoided. The decoupling can be achieved in a rigorous manner with the use of node-based basis functions. We provide a generic derivation of the method that is easily specialized for seismic and electromagnetic problems. The transformations between the optimization domain and the simulation domain are most effective if both domains can be described by rectilinear grids. A variable seabed depth causes difficulty. We introduce a transform from the true bathymetry to a flat seabed that solves this problem. The method is validated by application to synthetic and real electromagnetic data sets. The real data are acquired at the slow spreading Mohns Ridge located east of Greenland and southwest of Svalbard. We provide a discussion on the interpretation of these data for an inverse scheme using the transverse isotropy with a vertical symmetry axis approximation. We offer some insights on how to interpret inversion results in the case of exploration for marine minerals. The interpretation differs from a hydrocarbon exploration setting owing to the presence of vertical conductors due to the formation water circulation and vertical resistors due to volcanic intrusions.

Towards fast embedded moving horizon state-of-charge estimation for lithium-ion batteries

For state-of-charge (SOC) estimation with high precision, moving horizon estimation (MHE) has recently emerged as a competitive alternative to various Kalman filters or observers due to its significantly improved accuracy and robustness. However, MHE demands considerably higher computational complexity, preventing its deployment on a low-cost embedded microcontroller. To address this challenge, we propose a fast moving horizon SOC estimation algorithm to retain the benefits of MHE at a vastly reduced computational cost. In particular, we consider joint SOC and parameter estimation for an SOC-dependent equivalent circuit model subject to model mismatch. The proposed fast joint MHE (jMHE) algorithm performs a fixed number of Gauss–Newton (GN) iterations to approximate the fully converged solution. At each iteration, the GN Hessian matrix is factorized by exploiting its block tridiagonal structure to construct computationally efficient forward–backward recursions. To further speed up computations, another fast jMHE algorithm wtih an Event-Triggered Relinearization strategy (jMHE-ETR) is proposed to avoid refactorizing the GN Hessian matrix at each iteration. Using experimental datasets under different operating conditions, it is verified on both laptop and Raspberry Pi microcontroller that compared to the conventional optimal MHE solved with an off-the-shelf solver, the proposed fast jMHE and jMHE-ETR algorithms both have a slight loss of performance (still significantly better than extended Kalman filtering) while reducing its computational cost by an order of magnitude.

Elastic full-waveform inversion in tilted transverse isotropy media using Gauss Newton optimization

In anisotropic full waveform inversion (FWI), the underground medium is commonly assumed to be vertical transverse isotropy (VTI). However, in reality, the presence of stress and tectonic movements often leads to a nonzero tilt angle θt of the strata's symmetry axis. This introduces variations in the direction of the fast axis during the propagation of seismic waves. Therefore, it is more practical and beneficial to consider tilted transverse isotropy (TTI) media when dealing with complex geological structures, as it enhances the accuracy of imaging and inversion. However, the consideration of TTI media also introduces a significant challenge of parameter coupling, commonly known as crosstalk or trade-off. This refers to the situation where the update of one parameter affects and projects onto other parameters. To address this issue and improve the inversion accuracy, we incorporate the Hessian within the inversion process. The off-diagonal elements of the Hessian matrix specifically provide important information about the correlations between different parameters, which aids in their decoupling and mitigates the effect of crosstalk. In numerical experiments, we applied the Gauss-Newton (GN) method to TTI elastic FWI and compared the results with those obtained using the preconditioned conjugate gradient (P-CG) method.The inversion results indicate that the GN method can better alleviate the parameter coupling, making simultaneous inversion of multiple parameters possible. θt

Corn plant dry mass accumulation considering the previous crop by non-linear models

Corn is the most produced cereal in the world, used both in human and animal nutrition. This study aimed to compare the fit of the Logistic, Gompertz, and von Bertalanffy non-linear models to data on the accumulation of total dry mass, dry mass of stems, leaves, and ears in corn plants grown with straw mulch from common bean, millet, and Brachiaria brizantha in relation to the days after plant emergence. The assumptions of normality, homoscedasticity, and independence of residuals were checked by Shapiro-Wilk, Breusch-Pagan, and Durbin-Watson tests, respectively. The models were adjusted by the least squares method using the Gauss-Newton algorithm in the R software. The quality of the fit was evaluated based on the values of the coefficient of determination (R2), the residual standard deviation (RSD), the Akaike Information Criterion (AIC), and Bates and Watts curvature measures. The Logistic model presented the best fit for the dry mass of stems and ears, and the Gompertz model for the dry mass of leaves and total dry mass, based on the quality evaluators used.

On a Dynamic Variant of the Iteratively Regularized Gauss–Newton Method with Sequential Data

On a Dynamic Variant of the Iteratively Regularized Gauss–Newton Method with Sequential Data