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The purpose of this paper is to focus on the performance of three typical nonlinear least-squares estimation algorithms in atmospheric density model calibration.

The error of Jacchia-Roberts atmospheric density model is expressed as an objective function about temperature parameters. The estimation of parameter corrections is a typical nonlinear least-squares problem. Three algorithms for nonlinear least-squares problems, Gauss–Newton (G-N), damped Gauss–Newton (damped G-N) and Levenberg–Marquardt (L-M) algorithms, are adopted to estimate temperature parameter corrections of Jacchia-Roberts for model calibration.

The results show that G-N algorithm is not convergent at some sampling points. The main reason is the nonlinear relationship between Jacchia-Roberts and its temperature parameters. Damped G-N and L-M algorithms are both convergent at all sampling points. G-N, damped G-N and L-M algorithms reduce the root mean square error of Jacchia-Roberts from 20.4% to 9.3%, 9.4% and 9.4%, respectively. The average iterations of G-N, damped G-N and L-M algorithms are 3.0, 2.8 and 2.9, respectively.

This study is expected to provide a guidance for the selection of nonlinear least-squares estimation methods in atmospheric density model calibration.

The study analyses the performance of three typical nonlinear least-squares estimation methods in the calibration of atmospheric density model. The non-convergent phenomenon of G-N algorithm is discovered and explained. Damped G-N and L-M algorithms are more suitable for the nonlinear least-squares problems in model calibration than G-N algorithm and the first two algorithms have slightly fewer iterations.

The purpose of this paper is to present a novel gradient‐based iterative algorithm for the joint diagonalization of a set of real symmetric matrices. The approximate joint diagonalization of a set of matrices is an important tool for solving stochastic linear equations. As an application, reliability analysis of structures by using the stochastic finite element analysis based on the joint diagonalization approach is also introduced in this paper, and it provides useful references to practical engineers.

By starting with a least squares (LS) criterion, the authors obtain a classical nonlinear cost‐function and transfer the joint diagonalization problem into a least squares like minimization problem. A gradient method for minimizing such a cost function is derived and tested against other techniques in engineering applications.

A novel approach is presented for joint diagonalization for a set of real symmetric matrices. The new algorithm works on the numerical gradient base, and solves the problem with iterations. Demonstrated by examples, the new algorithm shows the merits of simplicity, effectiveness, and computational efficiency.

A novel algorithm for joint diagonalization of real symmetric matrices is presented in this paper. The new algorithm is based on the least squares criterion, and it iteratively searches for the optimal transformation matrix based on the gradient of the cost function, which can be computed in a closed form. Numerical examples show that the new algorithm is efficient and robust. The new algorithm is applied in conjunction with stochastic finite element methods, and very promising results are observed which match very well with the Monte Carlo method, but with higher computational efficiency. The new method is also tested in the context of structural reliability analysis. The reliability index obtained with the joint diagonalization approach is compared with the conventional Hasofer Lind algorithm, and again good agreement is achieved.

The purpose of this paper is to solve an inverse problem of structure recognition arising in eddy current testing (ECT) – type NDT. For this purpose, the space mapping (SM) technique with an extraction based on the Gauss‐Newton algorithm with Tikhonov regularization is applied.

The aim is to have a computationally fast recognition procedure of defects since the monitoring results in a large amount of data points that need to be analyzed by 3D eddy current model. According to the SM optimization, the finite element method (FEM) is used as a fine model, while the model based on an integral method such as the volume integral method (VIM) serves as a coarse model. This approach, being an example of a two‐level optimization method, allows shifting the optimization load from a time consuming and accurate model to the less precise but faster coarse surrogate.

The application of this method enables shortening of the evaluation time that is required to provide the proper parameter estimation of surface defects.

In this work only the specific kinds of surface defects were considered. Therefore, the reconstruction of arbitrary shapes of defects when using real measurement data from ECT system can be treated in further research.

The paper investigated the eddy current inverse problem. According to aggressive space mapping method, a suitable coarse model is needed. In this case, for the purpose of 3D defect reconstruction, the reduced VIM approach was applied. From a practical view point, the authors demonstrated that the two‐level inversion procedures allow saving of up to 50 percent CPU time in comparison with the optimization by means of regularized Gauss‐Newton algorithm in the same FE model.

The main purpose of this paper is to determine the discount function which better fits the individuals' preferences through the empirical analysis of the different functions used in the field of intertemporal choice.

After an in-depth revision of the existing literature and unlike most studies which only focus on exponential and hyperbolic discounting, this manuscript compares the adjustment of data to six different discount functions. To do this, the analysis is based on the usual statistical methods, and the non-linear least squares regression, through the algorithm of Gauss-Newton, in order to estimate the models' parameters; finally, the AICc method is used to compare the significance of the six proposed models.

This paper shows that the so-called q-exponential function deformed by the amount is the model which better explains the individuals' preferences on both delayed gains and losses. To the extent of the authors' knowledge, this is the first time that a function different from the general hyperbola fits better to the individuals' preferences.

This paper contributes to the search of an alternative model able to explain the individual behavior in a more realistic way.

This paper aims to gain the real-time terrain parameters of the battlefield for the evaluation of military vehicle trafficability. In military missions, improvements in vehicle mobility have the potential to greatly increase the military operational capacity, in which vehicle trafficability plays a significant role.

In this framework, an online terrain parameter estimation method based on the Gauss-Newton algorithm is proposed to estimate the primary terrain mechanical parameters. Good estimation results are indicated, unless the initial values involved are properly selected. Correspondingly, a method of terrain classification is then presented to contribute to the selection of the initial values. This method uses the wavelet packet transform technique for feature extraction and adopts the support vector machine algorithm for terrain classification. Once the terrain type is identified, advices can be given on the initial value selection referring to the empirical terrain parameters.

On the basis of a dynamic testing system suitable for real military vehicles, the proposed algorithms are validated. High estimation accuracy of the terrain parameters is indicated on sandy loam, and good classification performance is demonstrated on four tested terrains.

The presented algorithm outperforms the existing methods, which not only realizes the online terrain parameter estimation but also develops the estimation accuracy. Moreover, its effectiveness is confirmed by real vehicle tests in practice.

The purpose of the work is to provide a comprehensive review of the digital image correlation (DIC) technique for those who are interested in performing the DIC technique in the area of manufacturing.

No methodology was used because the paper is a review article.

no fundings.

Herein, the historical development, main strengths and measurement setup of DIC are introduced. Subsequently, the basic principles of the DIC technique are outlined in detail. The analysis of measurement accuracy associated with experimental factors and correlation algorithms is discussed and some useful recommendations for reducing measurement errors are also offered. Then, the utilization of DIC in different manufacturing fields (e.g. cutting, welding, forming and additive manufacturing) is summarized. Finally, the current challenges and prospects of DIC in intelligent manufacturing are discussed.

This paper aims to propose a fast and robust 3D point set registration method for pose estimation of assembly features with few distinctive local features in the manufacturing process.

The distance between the two 3D objects is analytically approximated by the implicit representation of the target model. Specifically, the implicit B-spline surface is adopted as an interface to derive the distance metric. With the distance metric, the point set registration problem is formulated into an unconstrained nonlinear least-squares optimization problem. Simulated annealing nested Gauss-Newton method is designed to solve the non-convex problem. This integration of gradient-based optimization and heuristic searching strategy guarantees both global robustness and sufficient efficiency.

The proposed method improves the registration efficiency while maintaining high accuracy compared with several commonly used approaches. Convergence can be guaranteed even with critical initial poses or in partial overlapping conditions. The multiple flanges pose estimation experiment validates the effectiveness of the proposed method in real-world applications.

The proposed registration method is much more efficient because no feature estimation or point-wise correspondences update are performed. At each iteration of the Gauss–Newton optimization, the poses are updated in a singularity-free format without taking the derivatives of a bunch of scalar trigonometric functions. The advantage of the simulated annealing searching strategy is combined to improve global robustness. The implementation is relatively straightforward, which can be easily integrated to realize automatic pose estimation to guide the assembly process.

In this second installment, the author addresses some of the problems associated with empirically validating contingent‐claim models for valuing risky debt. The article uses a simple contingent claims risky debt valuation model to fit term structures of credit spreads derived from data for U.S. corporate bonds. An essential component to fitting this model is the use of expected default frequency; the estimate of the firms' expected default probability over a specific time horizon. The author discusses the statistical and econometric procedures used in fitting the term structure of credit spreads and estimating model parameters. These include iteratively reweighted non‐linear least squares are used to dampen the impact of outliers and ensure convergence in each cross‐sectional estimation from 1992 to 1999.

The purpose of this paper is to propose a new method based on nonlinear least squares (NLS) for solving the parameters of nonlinear grey Bernoulli model (NGBM(1,1)) and to verify the proposed model using the case of employee demand prediction of high-tech enterprises in China.

First of all, minimising the square sum of fitting error of grey differential equation of NGBM(1,1) is taken as the optimisation target and the parameters of classic grey model (GM(1,1)) are set as the initial value of parameter vector. Afterwards, the structural parameters and power exponents are solved by using the Gauss-Newton iteration algorithm so as to calculate the parameters of NGBM(1,1) under given rules for ceasing the algorithm. Finally, by taking the employee demand of high-tech enterprises in the state-level high-tech industrial development zone in China as examples, the validity of the new method is verified.

The results show that the parameter estimation algorithm based on the NLS method can effectively identify the power exponents of NGBM(1,1) and therefore can favourably adapt to the nonlinear fluctuations of sequences. In addition, the algorithm is superior to the GM(1,1) model, grey Verhulst model, and Quadratic-Exponential smoothing algorithm in terms of the simulation and prediction accuracy.

Under the framework of solving parameters based on NLS, various aspects of NGBM(1,1) remain to be further investigated including background value, initial condition and variable structural modelling methods.

The parameter estimation algorithm based on NLS can effectively identify the power exponent of NGBM(1,1) and therefore it can favourably adapt to the nonlinear fluctuation of sequences.

According to the basic principle of NLS, a new method for solving the parameters of NGBM(1,1) is proposed by using the Gauss-Newton iteration algorithm. Moreover, by conducting the modelling case about employees demand in high-tech enterprises in China, the effectiveness and superiority of the new method are verified.

The paper aims to present an innovative solution for evaluation study of the dampness level of walls and historical buildings.

Electrical tomography enables one to obtain a distribution pattern of wall dampness. The application of modern tomographic techniques in conjunction with topological algorithms will allow one to perform very accurate spatial assessment of the dampness levels of buildings. The proposed application uses the total variation, Gauss–Newton and level set method to solve the inverse problem in electrical tomography.

Research shows that electrical tomography can provide effective results in damp buildings. This method can provide 2D/3D moisture distribution pattern.

The impact of this technique will be limited to inspection of the facility after floods or assessment of historical buildings.

The presented method could eventually lead to a much more effective evaluation of moisture in the walls.

The solution has commercial potential and could result in more cost-effective monitoring of historical buildings, which have an economic impact on society.

The authors propose a system for imaging spatial moistness of walls and historic buildings based on electrical tomography and consisting of a measuring device, sensors and image reconstruction algorithms.