Levenberg-Marquardt Iterative Algorithm Research Articles

Polytopic LPV modeling and gain scheduling [formula omitted] control of ball screw with position- and load-dependent variable dynamics

Ball screw drive (BSD) is a precision transmission mechanism widely used in high-precision positioning or tracking systems. The dynamic behavior of BSD varies with position and load, which causes tracking errors and poor robustness. Therefore, this paper proposes a polytopic linear parameter varying (LPV) model to express the varying dynamic behavior of BSD. The parameters of the LPV model are identified by the closed-loop frequency domain method and Levenberg–Marquardt iterative algorithm. Based on the polytopic LPV model, an LPV gain scheduling (GS) H∞ controller is proposed for the BSD with varying dynamics. Specifically, the controller is designed through polytope-based GS representation and mixed sensitivity synthesis. The most significant part is the proposal of a GS H∞ control algorithm to implement controller parameters that change with changing dynamics. Moreover, the stability of the closed-loop system is achieved by quadratic stabilization with state feedback. Finally, identification experiments and trajectory-tracking comparative experiments are carried out. The experimental results demonstrate that the proposed polytopic LPV modeling and GS H∞ control synthesis are effective in achieving accurate trajectory tracking and excellent robustness.

Phosphate adsorption on LDHs-biochar composite: Double-layer model for quantifying the contribution of ion exchange and ligand exchange.

The adsorption performance of layered double hydroxides (LDHs) is limited owing to self-aggregation. To avoid this and effectively control the eutrophication of water bodies, biochar (BC) was synthesized, herein, by pyrolyzing waste sheep manure at 500°C, and Ca-Al-LDHs were loaded on the surface via a coprecipitation method to obtain Ca-Al-LDHs-BC(CA) composites with varying LDH contents. The fitted maximum adsorption capacities of the CA-5%, CA-10%, CA-15%, and CA-20% samples (corresponding to samples with 5%, 10%, 15%, and 20% LDHs, respectively) were 10.21, 16.14, 22.40, and 28.47 mg g-1, which were (when converted into metal proportions) 1.48, 1.23, 1.15, and 1.13 times of that of single hydrotalcite, respectively. The double-layer model was fitted using the Levenberg-Marquardt iterative algorithm, which when combined with the characterization results, confirmed that the adsorption of phosphate ions by CA-BC occurred via the double-layer adsorption mechanism. Two types of direct adsorption were observed: ion exchange, which resulted in first-layer adsorption, and ligand exchange, which resulted in second-layer adsorption, with first-layer adsorption accounting for a higher proportion. This double-layer adsorption mechanism showed that LDHs-BC could achieve higher ligand exchange performance compared to that achieved using only LDHs.

Research on the multimodal fusion calibration method of the binocular visual system in a large-scale FOV

Calibration is vital for the binocular visual system. The high-precision measurement volume of the traditional binocular visual system is very small; therefore, it is difficult to measure large objects accurately. Accurate calibration of the binocular visual system is also extremely difficult in a large-scale field-of-view (FOV). Several attempts have been made to calibrate the binocular visual system in a large-scale FOV without recognizing the importance of depth information. A new method based on multimodal constraints has been proposed to calibrate the binocular visual system in a large-scale FOV whose height-width-depth is 2*2*2 . The method fuses multiple constraints, i.e. the distance error constraint, the reprojection error constraint, the epipolar error constraint, the spatial points error constraint, and the regularization constraint. An objective function that integrates the above constraints has been derived. The construction method of the global Jacobi matrix, the adaptive weight adjustment method, and the Levenberg–Marquardt iterative algorithm are used to minimize the objective function. Comparison experiments have been carried out to validate the performance of our proposed method by measuring a 1.4 m long calibration gauge. The results show that the root mean square (RMS) of the residual error of our method is 0.0929 mm, Zhang’s traditional method is 0.523 mm, and Xiao’s photogrammetric method is 0.348 mm. The RMS of our method is 82% less than that of Zhang’s method. Noise experiments show that the RMS of the residual error of our method is 45% less than Zhang’s method with 0.1 level noise inference, which verifies the stability and reliability of our method.

A High-Precision Indoor Positioning Scheme Based on Feature Code and Lighting Device

Visible light positioning is one of the schemes based on driving modulation to achieve high accuracy of indoor positioning. However, it has shortcomings in system deployment, maintenance, and scalability, which limits its wide application. We propose a high-precision positioning scheme based on high-transparency feature code and lighting devices. First, a feature-code mask is exploited to replace the driving modulation, which aims to reduce the complexity, improve the scalability, and realize high-precision and real-time positioning. Then, a two-dimensional (2-D) feature code is designed to detect the characteristics, which greatly increases the number of LED IDs and decreases the system complexity. Third, the Levenberg–Marquardt iterative algorithm with the constructed perspective-n-point model is applied to obtain the position of the camera. Experimental results show that the proposed scheme can obtain high-precision and real-time positioning. When the measuring height is 1.6 m, the average root-mean-square error (rmse) is 0.044 m. Moreover, when the height is 1.8 m and 2.0 m, the average RMSEs are 0.054 m and 0.064 m, respectively.

A Novel Fuzzy Controller for Visible-Light Camera Using RBF-ANN: Enhanced Positioning and Autofocusing.

To obtain high-precision for focal length fitting and improve the visible-light camera autofocusing speed, simultaneously, the backlash caused by gear gaps is eliminated. We propose an improved RBF (Radical Basis Function) adaptive neural network (ANN) FUZZY PID (Proportional Integral Derivative) position closed-loop control algorithm to achieve the precise positioning of zoom and focus lens groups. Thus, the Levenberg-Marquardt iterative algorithm is used to fit the focal length, and the improved area search algorithm is applied to achieve autofocusing and eliminate backlash. In this paper, we initially adopt an improved RBF ANN fuzzy PID control algorithm in the position closed-loop in the visible-light camera position and velocity double closed-loop control system. Second, a similar triangle method is used to calibrate the focal length of the visible-light camera system, and the Levenberg-Marquardt iterative algorithm is used to fit the relation of the zoom potentiometer code values and the focal length to achieve the zoom position closed-loop control. Finally, the improved area search algorithm is used to achieve fast autofocusing and acquire clear images. The experimental results show that the ITAE (integrated time and absolute error) performance index of the improved RBF ANN fuzzy PID control algorithm is improved by more than two orders of magnitude as compared with the traditional fuzzy PID control algorithm, and the settling time is 6.4 s faster than that of the traditional fuzzy PID control. Then, the Levenberg-Marquardt iterative algorithm has a fast convergence speed, and the fitting precision is high. The quintic polynomial fitting results are basically consistent with the sixth-degree polynomial. The fitting accuracy is much better than that of the quadratic polynomial and exponential. Autofocusing requires less than 2 s and is improved by more than double that of the traditional method. The improved area search algorithm can quickly obtain clear images and solve the backlash problem.

Parameter identification of fractional order Hammerstein model with two-stage piecewise nonlinearity based on iterative algorithms

This paper discusses identification of the fractional order Hammerstein model with colored noise. The static part of the Hammerstein model is a two-stage piecewise nonlinearity, while the dynamic part is a CARMA structure. We deduce the identification expression of the model through the definition of the Grünwald–Letnikov fractional differential. Then, two iterative algorithms are adopted to identify the unknown parameters. One of them is the Levenberg–Marquardt iterative algorithm, and the other is the particle swarm optimization iterative algorithm. The two algorithms are extended from the traditional integer order system identification field to the fractional order nonlinear colored noise system identification field. A numerical example and a case study of servo system identification are respectively presented to demonstrate the feasibility of the identification algorithms. It can be seen that the estimation errors of these two algorithms are relatively small, which reflects their good identification effect.

A Novel Classification Method to Random Samples for Efficient Reliability Sensitivity Analysis

Abstract Reliability sensitivity analysis is important to measure how uncertainties influence the reliability of mechanical systems. This study aims to propose an efficient computational method for reliability sensitivity analysis with high accuracy and efficiency. In this study, coordinates of some points on the limit state function are first calculated through Levenberg–Marquardt (LM) iterative algorithm, and the partial derivative of system response relative to uncertain variables is obtained. The coordinate mapping relation and the partial derivative mapping relation are then established by radial basis function neural network (RBFNN) according to these points calculated by the LM iterative algorithm. Following that, the failure samples can be screened out from the Monte Carlo simulation (MCS) sample set by the well-established mapping relations. Finally, the reliability sensitivity is calculated by these failure samples and kernel function, and the failure probability can be obtained correspondingly. Two benchmark examples and an application of industrial robot are used to demonstrate the effectiveness of the proposed method.

Precise and robust binocular camera calibration based on multiple constraints.

Precise calibration of a binocular vision system is the foundation of binocular vision measurement. In this paper, we propose a highly precise and robust binocular camera calibration method, which is devoted to minimize the error between the geometric relation of 3D reconstructed feature points and the ground truth, such as adjacent distance error, collinear error, and right-angle error. In addition, the reprojection error and epipolar are introduced to satisfy the homography relation and epipolar geometry theory better. We optimize all intrinsic parameters, extrinsic parameters, and distortion parameters to minimize the objective function, which is the sum of a series of nonlinear least squares terms. Levenberg-Marquardt iterative algorithm is used to find the optimal solution of the camera parameters. To test the precision and robustness of the proposed method, both actual measurement experiments and Gauss noise-adding experiments are carried out. The experimental results show that compared with the other two calibration methods in the contrast experiment, the distance measurement error, collinear error, and right-angle error are reduced dramatically. It is noticeable that in Gauss noise-adding experiments, the calibration parameters estimated by the proposed method are more stable.

Rigorous pulse detection from full-waveform airborne laser scanning data

Current discrete airborne laser scanning (ALS) systems suffer from a limited number of multiple returns and the loss of information about range estimation. To improve range resolution and accuracy, latest generation small-footprint, full-waveform laser scanning data were investigated and an approach developed to determine the number of targets within complex waveforms. The approach, termed rigorous Gaussian detection (RGD), is based on the popular Gaussian decomposition method but is implemented with rigorous estimates of initial values and a sophisticated iteration procedure. Second derivatives of waveforms and the number of samples on the edges of visible peaks were analysed to find overlapping targets. Weak pulses were detected where the residuals of Gaussian fitting were high and corresponding pulse widths were close to that of the transmitted pulse. The performance was compared with two other pulse detection techniques from commercial software, namely the centre of gravity (COG) method and the Gaussian pulse fitting (GPF) method with the Levenberg–Marquardt iterative algorithm. The results proved that the developed pulse detection method resolved multi-targets well. For example, in a sample of 201 dual-target waveforms, the RGD method correctly detected two targets in all the samples, considerably outperforming the COG and GPF methods, which achieved 57% and 67% success rates, respectively. When measuring the target heights using the different methods, the RGD method, with a root mean square error (RMSE) of 0.06 m, proved twice as accurate as the next best method, COG. The developed approach therefore compares favourably against the two commercial pulse detection methods considered, where their failure to detect hidden targets within complex waveforms and weak pulses resulted in a decrease of multi-target resolution, unreliable three-dimensional (3D) points, and also the loss of information from weak pulses.

Two-dimensional/three dimensional Hybrid Interstitial Diffuse Optical Tomography of Human Prostate during Photodynamic Therapy: Phantom and Clinical Results.

We have developed an efficient Levenberg-Marquardt iterative algorithm utilizing a three-dimensional field measurements coupled to a two-dimensional optical property reconstruction scheme. This technique takes advantage of accurate estimation of light distribution in 3D forward calculation and reduced problem size and less computation time in 2D inversion. Important advances in terms of improving algorithm efficiency and accuracy include use of an iterative general minimum residual method (GMRES) for computing the field solutions, application of the dual mesh scheme and adjoint method for Jacobian construction, and implementation of normalization scheme to reduce the absorption-scattering cross talk. The synthetic measurement data were calculated for a cubic phantom containing a single absorption anomaly and a single scattering anomaly. The model had a background of μa=0.03mm-1 and μs'=1.4mm-1. The absorption and scattering anomalies have the μa = 0.06 mm-1 and μs' = 2.0 mm-1. Five sources and 72 detectors are used per slice. A typical human prostate is composed of 6 slices. The reconstruction images successfully recover the both anomalies with good localization. Experiment data from tissue simulated phantom are also presented. The clinical DOT imaging was performed before photodynamic therapy based on the protocol. The preliminary results showed the reconstructed prostate μa varied between 0.025 and 0.07 mm-1 and μs' ranged from 1.1 to 2 mm-1. These results show that this new 2D-3D hybrid algorithm consistently outperform the 2D-2D or 3D-3D counterparts.

Non-fourier heat condution behavior in finite mediums under pulse surface heating

The present work considers transient heat conduction in a finite medium exposed to a pulse surface heating by using the generalized macroscopic conduction model. The analytical solution is derived by using Green's function method and finite integral transform technique. Calculations are performed to exhibit various behavior of thermal transports in the medium, such as wave, wavelike, and diffusion. By using the temperature solution, the inverse analysis is performed by nonlinear least-squares method for determining the two relaxation parameters and thermal diffusivity from a given temperature response. The nonlinear system of algebraic equations resulting from the sensitivity matrix is solved by the Levenberg–Marquardt iterative algorithm. The inverse analysis is utilized to estimate the relaxation parameters and the thermal diffusivity from the simulated experimental non-Fourier temperature response obtained by the direct calculation.

An Inverse Analysis to Estimate Relaxation Parameters and Thermal Diffusivity with a Universal Heat Conduction Equation 1

This paper presents an inverse analysis for simultaneous estimation of relaxation parameters and thermal diffusivity with a universal heat conduction model by using temperature responses measured at the surface of a finite medium subjected to pulse heat fluxes. In the direct analysis, the temperature responses in a finite medium subjected to a pulse heat flux are derived by solving the universal heat conduction equation. The inverse analysis is performed by a nonlinear least-squares method for determining the two relaxation parameters and thermal diffusivity. Here, the nonlinear system of algebraic equations resulting from the sensitivity matrix is solved by the Levenberg–Marquardt iterative algorithm. The inverse analysis is utilized to estimate the relaxation parameters and the thermal diffusivity from the simulated experimental non-Fourier temperature response obtained by direct calculation.

Geology-exploration endowment models for simultaneous estimation of discoverable mineral resources and endowment

A new type of model, referred to as a geology-exploration endowment model, is proposed in this paper. These models differ from conventional ones in that they simultaneously estimate discoverable mineral resources and endowment by extracting and utilizing geoscience information from both geological features and exploration factors. Geological measurements describe mineral endowment, while exploration variables describe the completeness of exploration, and together, they explain discoverable resources. Without incorporation of exploration factors to geological-endowment models, the estimation of endowment is generally biased. This paper presents two variations of such hybrid nonlinear models: Poisson-logistic (PL) and exponential-logistic (EL) for estimation of number of mineral deposits or prospects based upon the Arps and Roberts' discovery process model and assumptions of endowment distributions. The PL model is obtained by assuming that endowment follows a Poisson distribution and that the probability of mineral occurrences (≥ 1) is a logistic function with geological arguments. The EL model is derived similarly, except that endowment is assumed to be exponentially distributed. The PL model is demonstrated on both a synthetic example and a case study of epithermal gold-silver vein deposits in the Walker Lake quadrangle of Nevada and California. A map containing the estimated numbers of gold-silver mineral occurrences potentially discoverable in the Walker Lake quadrangle is produced. The parameter estimates for the PL model based on the Levenberg-Marquardt iterative algorithm are validated by using several statistical measures, such as theT-statistic, Box's bias, and goodness of fit. Both a synthetic example and a case study suggest that the Box's bias measure is useful for validation of the nonlinear estimates.

Inverse recovery of two moving dipoles from simulated surface potential distributions on a realistic human torso model.

We tested a procedure to recover two moving dipole (TMD) parameters from bidipolar potential distributions generated over the surface of a numerical human torso model, using 120 surface sampling points. The surface distributions were computed for either a finite homogeneous torso (T1), a finite torso with lungs (T2), or a finite torso with lungs and blood masses (T3). Inverse calculations were carried out to initially recover the multipole series components (15, 24, or 35 terms) using either a finite homogeneous torso (I1) or a finite torso with lungs (I2), and a least-squares difference procedure. Next, the TMD parameters were obtained by fitting these multipole series components (15 or 24 terms) to the multipole series components estimated from the Brody shift equations, using the Levenberg-Marquardt iterative algorithm and a series of initial estimates for the TMD solution. A simulation run involved 253 different input dipole-pair combinations and 20 initial estimates. The correct TMD solution almost always coincided with that yielding the minimum residue, which was also the solution obtained by the largest fraction of initial estimates. The lowest rms position error of 2.7 mm was obtained with a T1-I1 torso combination, and with 35 recovered multipole series components and 24 Brody shift equations. Larger errors were obtained using a lower number of recovered multipole series components and Brody shift equations, or pairs of parallel or antiparallel dipoles, or dipoles of unequal amplitude.