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The time difference of arrival (TDOA) method has traditionally proven effective for locating acoustic emission (AE) sources and detecting structural defects. Nevertheless, its applicability is constrained when applied to anisotropic materials, particularly in the context of fiber-reinforced composite structures. In response, this paper introduces a novel COmposite LOcalization using Response Surface (COLORS) algorithm based on a two-step approach for precise AE source localization suitable for laminated composite structures. Leveraging a response surface developed from critical parameters, including AE velocity profiles, attenuation rates, distances, and orientations, the proposed method offers precise AE source predictions. The incorporation of updated velocity data into the algorithm yields superior localization accuracy compared to the conventional TDOA approach relying on the theoretical AE propagation velocity. The mean absolute error (MAE) for COLORS and TDOA were found to be 6.97 mm and 8.69 mm, respectively. Similarly, the root mean square error (RMSE) for COLORS and TODA methods were found to be 9.24 mm and 12.06 mm, respectively, indicating better performance of the COLORS algorithm in the context of source location accuracy. The finding underscores the significance of AE signal attenuation in minimizing AE wave velocity discrepancies and enhancing AE localization precision. The outcome of this investigation represents a substantial advancement in AE localization within laminated composite structures, holding potential implications for improved damage detection and structural health monitoring of composite structures. [ABSTRACT FROM AUTHOR]

Accurate calibration of a Stewart platform is important for their precise and efficient operation. However, the calibration of these platforms using forward kinematics is a challenge for researchers because forward kinematics normally generates multiple feasible and unfeasible solutions for any pose of the moving platform. The complex kinematic relations among the six actuator paths connecting the fixed base to the moving platform further compound the difficulty in establishing a straightforward and efficient calibration method. The authors developed a new forward kinematics-based calibration method using Denavit-Hartenberg (DH) convention and used the Stewart platform "Tiger 66.1" developed in their lab for experimenting with the photogrammetry-based calibration strategies described in this paper. This system became operational upon completion of construction, marking its inaugural use. The authors used their calibration model for estimating the errors in the system and adopted three compensation options or strategies as per least-square method to improve the accuracy of the system. These strategies leveraged a high-resolution digital camera and off-the-shelf software to capture the poses of the moving platform's center. This process is non-invasive and does not need any additional equipment to be attached to the hexapod or any alteration of the hexapod hardware. This photogrammetry-based calibration process involves multiple high-resolution images from different angles to measure the position and orientation of the platform center in the three-dimensional space. The target poses and actual poses are then compared, and the error compensations are estimated using the least-square methods to calculate the predicted poses. Results from each of the three compensation approaches demonstrated noticeable enhancements in platform pose accuracies, suggesting room for further improvements. Given that "Tiger 66.1" is based on the general Stewart platform structure, the proposed calibration method holds promise for extension to machines operating on similar principles where non-invasive calibration is desirable. This study contributes to advancing the field of Stewart platform calibration, paving the way for more precise and efficient applications in various domains. [ABSTRACT FROM AUTHOR]

In this paper, a new hybrid numerical approach is presented that couples "ghost cell" based immersed boundary (IB) method with the finite volume lattice Boltzmann method (FVLBM). In the implementation process, the grid cells are classified into three types, i.e., " f l u i d c e l l ", " s o l i d c e l l " and " g h o s t c e l l ", where the " g h o s t c e l l " is the first layer of " s o l i d c e l l " near the " f l u i d c e l l ". As the wall boundary condition is reflected in the " g h o s t c e l l ", the high–accuracy reconstruction of variables in it will be the key point of present approach. Then, a FVLBM scheme is used to update the distribution function in the " f l u i d c e l l ", and a least square interpolation based formulation is derived to construct the distribution functions in it. Further, the bounce–back scheme embedded in the streaming–collision lattice Boltzmann method will be employed as the wall boundary condition. Besides, for the class of moving boundary problems, the construction of the distribution function in the " f r e s h c e l l " is also considered. A number of typical benchmarking incompressible viscous fluid flows over both stationary and moving objects are simulated to justify the present method, using obstacles ranging from a stationary and a translating circular cylinders, a rotationally oscillating cylinder, to two more complex flows around an oscillating cylinder in the stationary fluid and in the free–stream. Besides, the temporal and spatial accuracy also are testified by the simulation of Taylor–Couette flow. The obtained accurate simulation results demonstrate the capability of the present hybrid IB–FVLBM for computer simulations of both stationary and moving boundary problems in the incompressible flow regime. [ABSTRACT FROM AUTHOR]

The goal of this paper is to contribute a firm and outstanding program to nonlinear fractional Volterra integro-differential equations with the initial value problem on the basis of the reproducing kernel method (RKM). To a certain extent, the difficulty of preserving memory of fractional differential operators is reduced. At the beginning, the model can be converted to the equivalent fractional Volterra integro-differential problem with a singular kernel that is consistent with the characteristics of Caputo derivatives. Additionally, the quasi-Newton’s method (QNM) and the principles of the least-squares method (LSM) are used to linearize the model and obtain the operation matrix, respectively. Once again, the uniqueness of the ε approximate solution is proven at length. The convergence and error estimation of the new technique are also deliberated. In the final step, the effectiveness of the algorithm is demonstrated by numerical examples. [ABSTRACT FROM AUTHOR]

Investigations are conducted on electromagnetohydrodynamic (EMHD) flow and heat transfer in a third‐grade fluid flowing through large parallel plates, which are maintained at constant temperatures. The impact of convective heat transmission is disregarded since the space between the plates is small. The influence of viscous dissipation is considered. Despite being addressed for Newtonian fluids, the conduction problem with the viscous dissipation effect is not examined in third‐grade fluids for EMHD flow and heat transfer behavior. The least‐square method is adopted to solve nondimensional, nonlinear momentum and energy conservation equations to get the dimensionless velocity, temperature distribution, and heat flux. Temperature and heat flux are investigated in relation to the third‐grade fluid parameter, the Hartmann number, the electric field parameter, and the Brinkman number. The findings show a rise in the Brinkman number dramatically increases heat transfer from both walls, necessitating cooling of both plates. The heat flow from both walls increases as the parameters of third‐grade fluid increases. [ABSTRACT FROM AUTHOR]

In this paper, we study the inverse problem of finding the source for heat conduction from the integral observation and the final time one. Using least-square method, this problem is reformulated into the optimal one of minimizing the objective functional. The Fréchet differentiability and the derivative of the objective functional are derived via an adjoint problem. Some numerical examples for finding the necessary optimality conditions are presented. [ABSTRACT FROM AUTHOR]

The new iterative method of approximating the boundary trajectory of a short-focus electron beam propagating in a free drift mode in a low-pressure ionized gas under the condition of compensation of the space charge of electrons is considered and discussed in the article. To solve the given approximation task, the root-polynomial functions of the fourth and fifth order were applied, the main features of which are the ravine character and the presence of one global minimum. As an initial approach to solving the approximation problem, the values of the polynomial coefficients are calculated by solving the interpolation problem. After this, the approximation task is solved iteratively. All necessary polynomial coefficients are calculated multiple times, taking into account the values of the function and its derivative at the reference points. The final values of polynomial coefficients of high-order root-polynomial functions are calculated using the dichotomy method. The article also provides examples of the applying fourth-order and fifth-order root-polynomial functions to approximate sets of numerical data that correspond to the description of ravine functions. The obtained theoretical results are interesting and important for the experts who study the physics of electron beams and design modern industrial electron beam technological equipment.

The time difference of arrival (TDOA) method has traditionally proven effective for locating acoustic emission (AE) sources and detecting structural defects. Nevertheless, its applicability is constrained when applied to anisotropic materials, particularly in the context of fiber-reinforced composite structures. In response, this paper introduces a novel COmposite LOcalization using Response Surface (COLORS) algorithm based on a two-step approach for precise AE source localization suitable for laminated composite structures. Leveraging a response surface developed from critical parameters, including AE velocity profiles, attenuation rates, distances, and orientations, the proposed method offers precise AE source predictions. The incorporation of updated velocity data into the algorithm yields superior localization accuracy compared to the conventional TDOA approach relying on the theoretical AE propagation velocity. The mean absolute error (MAE) for COLORS and TDOA were found to be 6.97 mm and 8.69 mm, respectively. Similarly, the root mean square error (RMSE) for COLORS and TODA methods were found to be 9.24 mm and 12.06 mm, respectively, indicating better performance of the COLORS algorithm in the context of source location accuracy. The finding underscores the significance of AE signal attenuation in minimizing AE wave velocity discrepancies and enhancing AE localization precision. The outcome of this investigation represents a substantial advancement in AE localization within laminated composite structures, holding potential implications for improved damage detection and structural health monitoring of composite structures.

The main purpose of this paper is to approximate the solution of the nonlinear Volterra integral equation numerically in the reproducing kernel space. Consequently, in the study, combining Quasi-Newton's method and the least-square method, we develop a new method for solving this kind of equation. This technique transforms the nonlinear Volterra integral equation into a linear algebraic system of equations, which can be solved by using the least-square method breezily. At the same time, to ensure the preciseness of the method, we strictly analyze the existence and uniqueness of ε -approximate solution and its convergence. Finally, we illustrate the accuracy and reliability of this method by giving some examples. [ABSTRACT FROM AUTHOR]

For the primal-mixed form of the steady diffusion-reaction equation, a new conforming discontinuous finite element scheme is proposed by using the idea of discontinuous finite element method and the least-square method. Then the method is extended to the case of unsteady diffusion-reaction equation and a fully discrete conforming discontinuous finite element scheme is given. This scheme avoids the LBB condition and can be applied to polygon mesh. Under the energy norm, the optimal convergence order error estimates for the primary and flux variables are established. Finally, for the steady and unsteady equations, some numerical examples in general and convection dominated cases are given to verify the effectiveness of the method. [ABSTRACT FROM AUTHOR]

The new iterative method of approximating the boundary trajectory of a short-focus electron beam propagating in a free drift mode in a low-pressure ionized gas under the condition of compensation of the space charge of electrons is considered and discussed in the article. To solve the given approximation task, the root-polynomial functions of the fourth and fifth order were applied, the main features of which are the ravine character and the presence of one global minimum. As an initial approach to solving the approximation problem, the values of the polynomial coefficients are calculated by solving the interpolation problem. After this, the approximation task is solved iteratively. All necessary polynomial coefficients are calculated multiple times, taking into account the values of the function and its derivative at the reference points. The final values of polynomial coefficients of high-order root-polynomial functions are calculated using the dichotomy method. The article also provides examples of the applying fourth-order and fifth-order root-polynomial functions to approximate sets of numerical data that correspond to the description of ravine functions. The obtained theoretical results are interesting and important for the experts who study the physics of electron beams and design modern industrial electron beam technological equipment. [ABSTRACT FROM AUTHOR]

Copyright of Large Electric Machine & Hydraulic Turbine is the property of Large Electric Machine & Hydraulic Turbine Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In data analysis and signal processing, the recovery of structured functions from the given sampling values is a fundamental problem. Many methods generalized from the Prony method have been developed to solve this problem; however, the current research mainly deals with the functions represented in sparse expansions using a single generating function. In this paper, we generalize the Prony method to solve the sparse expansion problem for two generating functions, so that more types of functions can be recovered by Prony-type methods. The two-generator sparse expansion problem has some special properties. For example, the two sets of frequencies need to be separated from the zeros of the Prony polynomial. We propose a two-stage least-square detection method to solve this problem effectively. [ABSTRACT FROM AUTHOR]

A new least-squares method based on cubic B-spline functions is presented to solve regularized long-wave (RLW) equation numerically. An algebraic system of equations is obtained by employing the least-squares method based on cubic B-spline approximation for spatial discretization and the Crank–Nicolson technique for time discretization for integrating the RLW equation. The two test problems are implemented to show suitability of the proposed scheme. New results have been compared with those of some previous studies available in the literature. [ABSTRACT FROM AUTHOR]

High-resolution hyperspectral imagery has been one of the most fashionable tools using the push broom scanner in motion, particularly for the in-line measurement in industrial production of food and agricultural products. However, a distinct pattern of stripes can tend to impair the image quality that resulted from the non-uniformity among the sensing pixels, due to the inhomogeneity of imaging sensors in manufacturing, dark currents, and working conditions. Taking the pork as the measurement subject, this work aims to devise a de-stripe procedure for the relative radiance calibration using multiple standard reflectance panels. The specific procedure included the illumination of the standard panels to generate spatially uniform-distributed fluxes on the different levels into the camera, in order to gage the response of individual pixels on the imaging sensor. A polynomial fitting of sensor readouts on reflectance values was implemented to profile the response function of individual sensing pixels, and the compensation of all the sensing pixels for each wavelength, according to the response differences to a designated pixel as reference. A reflectance calibration was also provided to calculate the imaging subject reflectance using this procedure, according to the inverse of the fitted response function for the individual sensing pixels. Furthermore, the hyperspectral images of pork were selected to verify the de-stripe performance of the calibration procedure working on the third-order polynomial fitting with that of moment-matching using an intuitive visual evaluation aided with pseudo-color mapping, an objective profiling of the average digital number per column, as well as the maxima of stripe-index. In addition, a step-reflectance standard panel was used to measure the accuracy of the reflectance calibration on the regions of four reflectance values. Results showed that the subject spatial variation across the image columns was dropped along with the removal of stripe-noise, where the apparent pseudo edges were created, especially at the columns located in the transition from background to subject. There was a significant difference in moment matching in the image-columns average digital numbers of the same gray value after calibration. The calibration per individual pixel working on each wavelength substantially reduced the stripe noise, while no new noise was introduced. The spatial distributions in the original image were perfectly maintained as the image-columns average-digital-number profiles after de-stripe calibration, indicating a good agreement with those before. Aside from the compelling visual evidence, the procedure was also quantified in both the maxima of stripe-index after calibration and the lowness of reflectance error. Specifically, there was a 63.5% decrease in the stripe-index maxima on the hyperspectral images of pork. The reflectance calibration error was 0.003-0.089 for the four regions on the step-standard panel in the most stripe-stricken waveband 200, and 0.009-0.083 in a random waveband 300. The procedure of relative radiance calibration and the companion reflectance calibration can be widely expected to reduce the stripe-noise, while for the intact of subjects’ spatial details and precise reflectance values. The finding can be paving the way to better spatial visualization of quality indicators and attributes to the food and agricultural products when working on the images collected using push-broom hyperspectral imagery. [ABSTRACT FROM AUTHOR]

Copyright of Chinese Journal of Liquid Crystal & Displays is the property of Chinese Journal of Liquid Crystal & Displays and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In geophysical exploration, inversion is carried out on the observed data to generate a geophysical model, approximating the subsurface geological struc­ture. In the interpretation of magnetic data, the subsurface model parameters are found by a proper inversion scheme. Hence, it will be possible to obtain the entire parameters of any features (e.g. Dike) including depth, width, and location. In this paper, theoretical and field studies were carried out to interpret the total components of magnetic anomalies of dikes at the finite depth. Moreover, a least-squares approach was used for depth determination using anomalous magnetic data. Potential field data inversion can be achieved through many optimization techniques. This study, however, it is attempted to develop an efficient two-dimensional (2D) inversion algorithm based on the Ridge Regression routine. The developed method was programmed using Matlab software and applied to three sets of synthetic magnetic data containing different percent of random noise to find out how good the results are. It was found that the proposed 2D inversion method can produce an accurate subsurface model that precisely explains the synthetic data in each case of data inversion. Finally, the method was applied to the real total magnetic field (TMF) data of Moghan Sedimentary basin. In that case, the estimated sedimentary basement depths were found to be in good agreement with that of the seismic data acquired before.

Formal concept analysis has shown much potential in supporting personalized learning. This paper is motivated by several application scenarios of concept lattices in supporting mathematics education. The aim of the paper is to develop a scheme for designing problem-chains based on concept lattices and provide evaluation methods towards steadiness of the corresponding learning processes. Particularly, a model is developed to study the sensitivity of conversion from effort on problems to efficacy on knowledge/skills. Then the notion of successive trails is introduced to describe means-end chains of learning states. Towards steadiness of the corresponding learning processes, evaluation methods are developed and data experiments are conducted from aspects of effort on problems, efficacy on knowledge/skills and conversion sensitivity. Moreover, the notion of conceptual paths is introduced in order to describe personalized learning strategies. Subsequently, a scheme for designing problem-chains is given based on conceptual paths and similarity measuring. Finally, a method of evaluating the steadiness of problem-chains is proposed by taking advantage of linear regression analysis on problem-chains. [ABSTRACT FROM AUTHOR]

Strip actuators have attracted tremendous attention in bionics due to the controllable deformation under various stimuli. However, it is currently hard to compare their performance owing to the different approaches for evaluating their actuation. Most of the studies determine the maximum or average value of the bending angle or strain, the deformation profile of the entire actuator strip was not quantified. In this study, a versatile method was proposed to evaluate the bending profile of typical strip actuators with bending deformation, thus analyzing the actuation performance. This method has been verified by synthetic curves, and less than 2% of global error was found. We have also demonstrated the implementation of this method for examining the actuation of typical strip actuators and showed that it can also be used for comparing the performance of different actuators prepared from other studies.

Heat transfer in a non-Newtonian third-grade fluid, flowing under the action of pressure gradient and shear, through two parallel plates, is considered. The upper plate moves with a constant velocity. Constant wall heat fluxes are applied to the plates. Effect of viscous dissipation is included, which has a major role in heat transfer of non-Newtonian fluids. The governing equations are nonlinear and are solved semi-analytically by using the least-square method (LSM). Then, using the solution for velocity in the energy equation, the solution is obtained by a direct integration process. Further, approximate analytical solutions are obtained by the perturbation method, which validates the results generated by the LSM. The effects of the third-grade fluid parameter on the velocity and temperature and also on the physical quantity, such as Nusselt's number, are discussed. Further, viscous dissipation effects on the temperature distribution have been analyzed. Observations show that the movement of the upper plate results in a significant decrease in temperature near the upper plate. For the unit heat flux ratio, the temperature difference between the surface and fluid is more at the upper surface due to the enhanced convective heat transfer caused by the moving upper plate. Nusselt's number increases significantly with an increase in the heat flux ratio. [ABSTRACT FROM AUTHOR]

In this article, we follow a thorough matrix presentation of material parameter identification using a least-square approach, where the model is given by non-linear finite elements, and the experimental data is provided by both force data as well as full-field strain measurement data based on digital image correlation. First, the rigorous concept of semi-discretization for the direct problem is chosen, where—in the first step—the spatial discretization yields a large system of differential-algebraic equation (DAE-system). This is solved using a time-adaptive, high-order, singly diagonally-implicit Runge–Kutta method. Second, to study the fully analytical versus fully numerical determination of the sensitivities, required in a gradient-based optimization scheme, the force determination using the Lagrange-multiplier method and the strain computation must be provided explicitly. The consideration of the strains is necessary to circumvent the influence of rigid body motions occurring in the experimental data. This is done by applying an external strain determination tool which is based on the nodal displacements of the finite element program. Third, we apply the concept of local identifiability on the entire parameter identification procedure and show its influence on the choice of the parameters of the rate-type constitutive model. As a test example, a finite strain viscoelasticity model and biaxial tensile tests applied to a rubber-like material are chosen. [ABSTRACT FROM AUTHOR]

In this paper, the gas pollutants in motor vehicle exhaust are taken as the research object. The diagnostic index system of motor vehicle gas pollutants on environmental pollution is constructed, based on the environmental pollution caused by motor vehicle exhaust. The emission intensity of various types of vehicles was studied. The least-square method is used to construct the diagnostic functions of different types of vehicle gas pollutants; the vehicle emission factors of different types of motor vehicle gas pollutants are obtained. By exploring the spatial–temporal correlation of vehicle emissions under traffic conditions, uncertainty mathematical theory is used to establish a spatial–temporal diagnosis model of vehicle gas pollutants on environmental pollution, and multiple correlation coefficients are used to conduct accuracy test. The research results can not only determine the pollution problem of motor vehicle emissions to the environment but also effectively evaluate the emission level of gas pollutants in the exhaust gas of motor vehicles. The application results show that the spatial–temporal diagnostic model of vehicle gas pollutants for environmental pollution has better guiding significance and practical value in solving environmental pollution problems. [ABSTRACT FROM AUTHOR]

In this article, a new design approach for the wideband transformer with frequency-dependent complex loads is proposed, which is based on the least-square method and the generalized modified small reflection theory (MSRT) with proper electrical parameters. Compared with the wideband transformers based on other approaches such as the generalized MSRT and transmission line theory, the proposed ones feature easy design, compact size, and wide bandwidth. For validation, several wideband transformers with frequency-dependent complex loads are designed, simulated, and measured. The measured results are consistent with the calculated and simulated results, and a wideband transformer with a fractional bandwidth of 68.5% (defined by 15-dB return loss) and an overall size of $0.025\lambda _{g}^{2}$ is achieved. In addition, when applied to the design of wideband Wilkinson power divider, a fractional bandwidth of 110% (defined by 25-dB isolation) and an overall size of $0.069\lambda _{g}^{2}$ are attained. [ABSTRACT FROM AUTHOR]

Thermal conductivity of concrete greatly influences the heat transfer of buildings and affected by many factors. This paper presents a prediction model for thermal conductivity of concrete by adopting the theory of Wiener bounds and considering concrete to have four components (water, air, aggregate, and cement mortar). The proposed model considers the combined effects of porosity, water saturation, and the volume fraction of aggregate on the thermal conductivity of concrete by weighting parameters of η 1 , η 2 , η 3 , respectively. By adjusting the weighting parameters of each component, the model can consider the influence of various factors on the thermal conductivity of concrete more comprehensively. Thermal conductivity of each component and expression of weighting parameters are determined by literature and experiments. The proposed model has been verified by the measured thermal conductivity of concrete under different porosities, water content, and volume fractions of aggregate with the prediction accuracy of ± 12 % . Finally, the regularity of the change in the thermal conductivity of concrete with porosity, water saturation, the volume fraction of aggregate, and temperature is analyzed. [ABSTRACT FROM AUTHOR]

In recent years, the matrix enhancement and matrix pencil method (MEMP) as well as the forward-backward MEMP (FBMEMP) have been successfully applied to reduce the number of antenna elements in the single-pattern planar arrays. This article aims to extend the MEMP and FBMEMP to the synthesis of sparse planar arrays with multiple patterns. The generalized MEMP (GMEMP) first constructs an enhanced matrix for each target pattern according to their data samples, respectively, and then these enhanced matrices are used to form a composite Hankel block matrix. After that, two sets of poles corresponding to two sets of reconstructed location coordinates can be extracted from the principal eigenvectors of the composite Hankel block matrix by the matrix pencil method. The randomized singular value decomposition and Hankel matrix decomposition method are used to accelerate the above extraction process. Then, we make use of improved matching algorithm to pair the two sets of position coordinates to obtain 2-D coordinates. Finally, we use the least-square method to obtain the excitations of sparse planar array elements, which makes the reconstruction process of multiple patterns more stable and accurate. Apart from the above, the GMEMP is also extended to the synthesis of multiple shaped-beam patterns using the generalized forward-backward matrix enhancement and matrix pencil method (GFBMEMP). A series of representative numerical examples show that the proposed methods can reduce the number of elements in the planar arrays efficiently while maintaining the accuracy of all the patterns to be synthesized. [ABSTRACT FROM AUTHOR]

In this article, several aspects of material parameter identification are addressed. We compare several methods to identify material parameters of a constitutive model for small strain, linear elastic transverse isotropy based on experimental data of specimens made from composite plates. These approaches range from identifying the five material parameters from purely analytical considerations to the fully numerical identification on the basis of finite elements and various data provided by digital image correlation (DIC). The underlying experimental tests range from purely uniaxial tensile tests with varying fiber orientation to shear and compression tests. A specific measuring instrument has been developed for the latter tests to obtain unique material parameters—motivated by the concept of local identifiability. Besides, we compare the numerical differentiation, which is the common procedure in parameter identification, with the fully analytical derivation of sensitivities within the DIC/FEM approach. [ABSTRACT FROM AUTHOR]

The accuracy of cooperative localisation can be severely degraded in non‐line‐of‐sight (NLOS) environments. To mitigate the NLOS errors, the cooperative localisation problem based on time of arrival (TOA) under the mixed line‐of‐sight (LOS)/NLOS conditions is addressed. By studying the topological relationship between nodes, a TOA NLOS mitigation cooperative localisation algorithm based on the topological unit is proposed. This algorithm is implemented under the classical multidimensional scaling framework. The adjacent topological unit of NLOS measurements are successfully identified by using the LOS matrix, and the NLOS measurements are re‐estimated using topological units. The least‐square method is used to transform the relative coordinates into absolute coordinates depending on the location of the anchor nodes. Compared to the existing methods, by employing the topological unit, this algorithm only requires the number of LOS anchor nodes to be 2 in the two‐dimensional plane, and the better localisation performance can be achieved. Simulation results show that the proposed method works well for both the sparse and dense NLOS environments. [ABSTRACT FROM AUTHOR]

The behavior of a nonlinear dynamic system under arbitrary excitation can be represented by the Volterra series if the Volterra kernels of different orders are known. This study presents a methodology for a direct estimation of the Volterra kernel coefficients up to the second-order using prepared data obtained by running a time-domain analysis of the system of interest. To avoid potential problems during kernel estimation, the Volterra kernel is expanded into a polynomial series using the Laguerre polynomials, and the coefficients of the Laguerre polynomials are then estimated using a least-square method. A nonlinear oscillator with a quadratic stiffness term is introduced, and the methodology is applied to check the applicability and accuracy. The methodology is applied to a more realistic engineering problem of a simplified riser under irregular wave excitation. [ABSTRACT FROM AUTHOR]

Summary: In this paper, a sensitivity‐based finite element (FE) model updating method using singular value decomposition (SVD) of frequency response function (FRF) is introduced. An exact sensitivity equation is proposed by incorporating measured responses of a damaged structure in the mathematical formulations. A set of incompletely measured natural frequencies of a damaged structure and mode shapes of the intact structure are used to deal with incomplete measurement without the implementation of FE model reduction or data expansion algorithms. The insights provided from the variation of SVD of transfer functions are used for the selection of proper updating frequency ranges. The appropriate arrangement and assembly of SVD‐based sensitivity equations are discussed to achieve more accurate model updating results. The solution of the developed sensitivity equation is obtained by the linear least‐square (LS) method and imposing unbiased side constraints on the design variables. The proposed method was examined numerically on the FE model of a 2D truss model and experimentally on a concrete beam. Low‐frequency ranges, including ranges around the first sixth vibration modes for numerical cases and ranges around the first three vibration modes for experimental cases, are successfully implemented for damage detection. The numerical and experimental results prove its high sensitivity for the cases of low severity and distributed damages and its robustness against high levels of measurement, natural frequency, and mass modeling errors. [ABSTRACT FROM AUTHOR]

Based on the study of existed least-squares and weighted least-squares phase unwrapping methods, an improved weighted least-squares algorithm based on unwrapping phase error compensation is proposed. First, the conventional weighted least-squares method is used to get the initial result of phase unwrapping. Then the unwrapping result is optimised by iterative compensation of phase unwrapping error. In addition, for the reasonable selection of the times of iteration, an iterative mechanism is designed to avoid the redundant or insufficient compensation caused by too many iterative times and too few. Compared with the traditional weighted least-square method, by using the proposed method, the global influence of phase noise is constrained by weighted processing, and meanwhile, the accuracy of phase unwrapping is greatly improved by iterative error compensation. The simulation results confirm the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

Uncertain differential equation has become an important tool to deal with uncertain dynamic systems such as finance, control and medical fields. The paper aims to study the problem of estimating unknown parameters in uncertain differential equations (UDEs). Least-square method is introduced to estimate unknown parameters of a class of simple UDEs. Further, two least-square estimators of a simple UDE are obtained. The simulation results show that the proposed method is feasible for estimating unknown parameters of some UDEs. [ABSTRACT FROM AUTHOR]

In this paper, a novel physics-informed neural networks (PINNs) called deep reduced-order least-square (ROLS) is proposed. The deep ROLS is a combination of reduced-order and least-square methods in the context of PINN methodology. The key idea of the deep ROLS is to convert a higher-order PDE to a system of lower-order PDEs by using primary and secondary variables, then the loss function constituted by integrals of corresponding squared residuals over the problem domain is minimized. Specifically, the squared residuals are established based on L 2 norm of respective reduced-order PDE terms, and the Gauss–Legendre quadrature rule is applied to approximate their integrals. A multi-network structure is also designed, in which each sub-network serves as one field variable corresponding to each reduced-order PDE. Moreover, this work proposes a scheme to handle both essential and natural boundary conditions (BCs) directly. The deep ROLS demonstrates its better advantages in comparison to original PINN method in terms of solution accuracy, computational cost and data efficiency for several beam bending problems having continuous and discontinuous solutions. • Proposes a novel framework of PINN for high-order PDEs. • The deep reduced order least square for non-differentiable problems. • Imposes all boundary conditions inside neural networks. • Approximate multi-variables simultaneously. [ABSTRACT FROM AUTHOR]

In recent years, Pedo-Transfer Functions (PTFs) have become a commonly used tool to predict the hydraulic properties of soil. As an important index to evaluate the function of forest water conservation, the prediction of saturated hydraulic conductivity (KS) on the regional scale is of great significance to guide the vegetation construction of returning farmland to forest area. However, if the published PTFs are directly applied to areas where the soil conditions are different from those where the PTFs are established, their predictive performance will be greatly reduced. In this study, 10 basic soil properties were measured as input variables for PTFs to predict KS in the three watersheds of Taergou, Anmentan, and Yangjiazhai in the alpine frigid hilly region of Qinghai Province, China. The parameters of the eight published PTFs were modified by the least-squares method and new PTFs were also constructed, and their prediction performance was evaluated. The results showed that the KS of coniferous and broad-leaved mixed forests and broad-leaved pure forests in the study area were significantly higher than those of pure coniferous forests, and grassland and farmland were the lowest (p > 0.05). Soil Organic Matter plays an important role in predicting KS and should be used as an input variable when establishing PTFs. The Analysis-Back Propagation Artificial Neural Network (BP ANN) PTF that was established, with input variables that were, Si·SOM, BD·Si, ln2Cl, SOM2, and SOM·lnCl had a better predictive performance than published PTFs and MLR PTFs.

Based on the study of existed least-squares and weighted least-squares phase unwrapping methods, an improved weighted least-squares algorithm based on unwrapping phase error compensation is proposed. First, the conventional weighted least-squares method is used to get the initial result of phase unwrapping. Then the unwrapping result is optimised by iterative compensation of phase unwrapping error. In addition, for the reasonable selection of the times of iteration, an iterative mechanism is designed to avoid the redundant or insufficient compensation caused by too many iterative times and too few. Compared with the traditional weighted least-square method, by using the proposed method, the global influence of phase noise is constrained by weighted processing, and meanwhile, the accuracy of phase unwrapping is greatly improved by iterative error compensation. The simulation results confirm the superiority of the proposed method.

Let X = X ∪ Z be a data set in ℝD, where X is the training set and Z the testing one. Assume that a kernel method produces a dimensionality reduction (DR) mapping 𝔉: X → ℝd (d ≪ D) that maps the high-dimensional data X to its row-dimensional representation Y = 𝔉(X). The out-of-sample extension of dimensionality reduction problem is to find the dimensionality reduction of X using the extension of 𝔉 instead of re-training the whole data set X. In this paper, utilizing the framework of reproducing kernel Hilbert space theory, we introduce a least-square approach to extensions of the popular DR mappings called Diffusion maps (Dmaps). We establish a theoretic analysis for the out-of-sample DR Dmaps. This analysis also provides a uniform treatment of many popular out-of-sample algorithms based on kernel methods. We illustrate the validity of the developed out-of-sample DR algorithms in several examples.

Nanoindentation is a technique commonly used to measure the mechanical properties of thin films even at depths less than 1 μ m. In fact, the characterization is based on the study of the load/displacement curves resulting from the nanoindentation test. We aim to use the backtracking search optimization algorithm (BSA) to improve the extraction of P(h) curves performed by nanoindentation on galvannealed Fe-Zn coating in terms of precision and dispersion. Indeed, the originality of this study is not limited only to the P(h) curve extraction methods, but also to its application in modeling the reverse approach for the case of Fe-Zn coating deposited on a Dual-Phase DP600 steel substrate. Indeed, the BSA approach showed more precision (with respect to the determined mean value) and less dispersion (magnitude of error around the identified mean value) compared to the Least-squares approach. The average error with the BSA and LS methods is respectively 0.89% and 3.16% for the yield stress $\left({{\boldsymbol{\sigma }}}_{{\boldsymbol{Y}}}\right)$ and 3.17% and 7.93% for the strain hardening exponent (n). This reduced the error variability in the prediction of the constitutive law to 72% and 60% for ( ${{\boldsymbol{\sigma }}}_{{\boldsymbol{Y}}}$ ) and n , respectively. Thus, we solved the problems of accessibility, uniqueness of the solution, precision (+10%) and dispersion (−85%) of the required prediction models for the Fe-Zn coating behavior.

In this paper, a working-process simulation model was established, and the characteristics regarding the diesel engine maximum output power were analyzed under different limiting parameters. The design margin of the marine diesel engine is obtained through numerical and experimental study. Then, the simulation model and single cylinder diesel engine test were used to investigate the theoretical determination method of limiting characteristic lines and design margin area. It can be found that using least-square method to fit the calculation results can achieve quantitative analysis of limiting characteristics, and then the design margin area can be confirmed. The analysis results show that the maximum output power of the diesel engine is limited by in-cylinder pressure, turbine speed and exhaust temperature. The limiting parameters of maximum output power are different at different speeds, and the trend with speed of maximum output power are also different under different limiting parameters. Furthermore, the analysis of the operating area shows that the margin of the marine diesel engine at rated speed is about 27%, and there is a large design margin when operating at high speed. [ABSTRACT FROM AUTHOR]

This paper proposes a class of simple but efficient control variate method for pricing derivatives under multiple factor models including stochastic volatility and stochastic interest rate model. The control variate can help us to obviously reduce the error of Monte Carlo simulation. Briefly speaking, we construct a virtual asset with deterministic volatility and deterministic interest rate which has high correlation with the original underlying asset based on the method of least square, and use derivative written on the virtual asset as control variate in pricing derivative written on the original underlying asset. Some theoretic results can help us to understand the mechanism of a control variate. Numerical examples show that simulation error is significantly reduced by our method. The advantage of our method is that it has no analytic form request for the underlying asset model, so the method is flexible to deal with and broadly applicable for derivative pricing. [ABSTRACT FROM AUTHOR]

The error sources that cause the pointing error are briefly analyzed to check whether the spatial static pointing error of a newly developed optical testing target satisfies the design index of 5′, and a pointing error model of target mechanism is established by the homogeneous coordinate transformation method. The azimuth and elevation errors of target are calibrated using Leica total station with high precision, and the pointing error of target is further synthesized. The calibrated results reveal that the maximum spatial static pointing error, θmax, is 275″, the mean value, θ, is 165.9″, and the square root, σθ, is 71.5″. In order to further improve the pointing accuracy of target, the least square method is used to fit the coefficients in the error model based on the calibrated data samples, and the calculated error models are used as the correction models of azimuth and elevation errors. When the pointing errors are corrected by using the proposed models, the average pointing error values of target mechanism at calibration points and the specific orbit are 21.1″ and 20.9″, respectively, and the root mean square are 10.6″ and 7.2″, respectively, which indicates that the static pointing error of the new target is greatly improved after error correction. [ABSTRACT FROM AUTHOR]

This work presents numerically derived regression models for evaluating the thermal efficiency and fluid exit temperature of a solar flat-plate collector (FPC), when water, 20% glycol-water or 40% glycol-water is used as the heat transfer fluid. A set of reliable samples of all the contributing parameters, chosen from the presented analytical model, were generated using the Latin hypercube sampling technique over a realistic range of values. The regression models were developed by fitting a response curve, using the least-squares method, to the simulation results. The proposed models were then validated by comparing the predicted results with those already published in the literature. The coefficients of determination (R2) for the efficiency models and fluid exit temperature models were found to exceed 97 and 93%, respectively. Sensitivity analysis, based on the elasticity of parameters in the statistically standardized version of these models, was also performed to identify the most influential design, operational and natural parameters. The effects of these parameters on FPC performance are quantified and discussed in detail. [ABSTRACT FROM AUTHOR]

Abstract We reviewed eight commonly used equilibrium adsorption models and examined their underlying assumptions, fitting qualities, and parameter stabilities. We compared several objective functions that have been applied to curve fitting analysis and a few statistics tests that have been performed to evaluate regression quality. The iteratively reweighted least squares algorithm was selected as the most suitable regression method for adsorption models in the presence of heteroscedasticity. The fraction of unexplained variance was selected to indicate the model fitting quality. Two sources of parameter instability were identified: residue instability and function instability. While the definition of the instability caused by residue is well established, we are the first to consider the instability caused by an adsorption model. The models discussed in this article can be applied to many surfactants, such as normal alcohols, polyglycol ethers, and sodium dodecyl sulfate at different salt concentrations. Our results show that both the model fitting quality and parameter instability increase with the number of parameters subject to curve fitting. For the Frumkin-type of reorientation model, the parameter instability can be as high as 25%. The high degree of instability in some complicated adsorption models may invalidate the estimated parameters. Therefore, additional measurements or simulations are required for complicated models to extract reliable model parameters. Graphical abstract Unlabelled Image Highlights • Classic, reorientation and ionic equilibrium surface tension models are reviewed. • Methods of curve fitting and evaluating are compared. • A rigorous definition of parameter instability is proposed. • Fitting qualities and stabilities of different models are discussed. • Potential solutions for parameter instability are considered. [ABSTRACT FROM AUTHOR]

In this paper, we propose a mathematical model to evaluate the transmission of Tuberculosis with drug-resistant strains and with drug-sensitive strains. Based on the epidemic data from Chinese Center for Disease Control and Prevention, we first estimate the values of parameters in the model. Then the basic reproduction number of TB infection in the mainland China is calculated to be 1. 0 5 5 8. Since the basic reproduction number is greater than 1 , Tuberculosis spreads as an endemic in mainland China. Through our investigations, the basic reproduction number associated with drug-sensitive strains is less than 1, but the number of individuals infected by drug-resistant strains will still increase quickly, thus the epidemic is not under control. Moreover, increasing the vaccination coverage rate for newborns is not always beneficial for controlling TB prevalence in China. Whether vaccination effect is positive or negative depends on the relapse rate from the recovered state to the infected state. In summary, improving sanitation conditions, introducing efficient measures to detect the disease, and keeping the public informed about how to lower the chance of being infected and the current epidemic situation are essential in slowing down or eliminating Tuberculosis transmission. [ABSTRACT FROM AUTHOR]

Subject of Research. The paper deals with the problems of higher order aspherical surfaces approximation using different equation types. The objects of research are two types of equations for higher order aspherical surfaces description used in different software for optical systems design (SАRО, OPAL, ZEMAX, CODE-V, etc.) and dependent on z-coordinate or on a radial coordinate on the surface. Conversion from one type of equations to another is considered in view of application in different software for optical systems design. Methods. The subject matter of the method lies in usage of mean square method approximation for recalculation of high-order aspherical surface. Iterative algorithm for recalculation is presented giving the possibility to recalculate coefficients for different types of equations with required accuracy. Recommendations are given for choosing recalculation parameters such as the number of result equation coefficients, the number of points for recalculation and point allocation on a surface. Main Results. Example of recalculation for aspherical surface and accuracy estimation, including result aberration comparison between initial surface and recalculated surface are presented. The example has shown that required accuracy of surface representation was obtained. Practical Relevance. This technique is usable for recalculation of higher order aspherical surfaces in various types of software for optical systems design and also for research of optimal higher order aspherical surfaces description.