Damped Least-squares Method Research Articles

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.

Differential ray tracing for an efficient computation of the Jacobian in the damped least-squares algorithm

We present a framework for the optimization of optical systems based up on the damped least-squares method and differential ray tracing. First, a mathematical description for the differentiation of the ray-surface intersection is introduced. It is observed that the structure of the optimization variables and operands can be exploited such that the Jacobian for the damped least-squares algorithm can be computed in the same computational complexity as the primal ray tracing for both forward and reverse mode algorithmic differentiation. To demonstrate the advantages of the method a freeform mirror system is analyzed.

Ambient noise tomography of a linear seismic array based on an improved Voronoi tessellation

Ambient noise tomography, when applied to a dense linear seismic array, has the capability to provide detailed insights into the fine velocity structures across diverse tectonic settings. The linear station arrangement naturally generates parallel and concentrated ray paths along the array trend. This unique geometry requires specific optimization of the inversion methodology and model parameterization. The Bayesian-based transdimensional inversion method, characterized by its fully non-linear nature and high degree of freedom in parameter settings, offers a powerful tool for ambient noise inversion. To effectively adapt this method to a linear array layout, we propose a modification to the Voronoi cell tessellation built in the transdimensional method. By introducing spatial priority to the Voronoi kernels, we strategically increased the density of Voronoi cells along the direction of the array. We then applied the modified approach to a linear seismic array in the North China Craton and validated its robustness through phase velocity images and resolution tests. Our improved non-uniform sampling technique in the 2-D model space accelerates convergence while simultaneously enhancing model accuracy. Compared with the conventional damped least-squares method, the proposed algorithm revealed a shear-wave velocity map with notable low-velocity anomalies situated in the middle and lower crust beneath the borders of the Ordos block and its surrounding orogenic belt. Aligned with the crustal structures revealed by receiver function and electrical imaging, our findings indicated that the western and eastern margins of the Ordos block had experienced intensive crustal wedge deformation and re-melting, respectively.

Early Identification of Abnormal Regions in Rock-Mass Using Traveltime Tomography

Early identification of abnormal regions is crucial in preventing the occurrence of underground geotechnical disasters. To meet the high-accuracy detection requirements of underground engineering, this paper proposes a tomography method for abnormal region identification in complex rock-mass structures that utilizes traveltime tomography combined with the damped least-squares method and Gaussian filtering. The proposed method overcomes the limitation of velocity difference in empty region detection and mitigates the impact from isolated velocity mutation in the iteration. Numerical and laboratory experiments were conducted to evaluate the identification accuracy and computational efficiency of forward modeling, including the shortest-path method (SPM), dynamic SPM (DSPM), and fast sweeping method (FSM). The results show that DSPM and FSM can clearly detect abnormal regions in numerical and laboratory experiments. Field experiments were conducted in the Shaanxi Zhènào mine and achieve the reconstruction of the underground roadway distribution. This paper not only realizes the application of abnormal region identification using traveltime tomography but also provides new insight into potential hazards detection in underground geotechnical engineering.

Analytical modelling of ultra-thin white topping cement concrete overlay on bituminous concrete pavement using ANSYS

PurposeThe ultra-thin white topping (UTW) is a cement concrete overlay of the thickness of 50–100 mm on bituminous concrete pavements with surface failures. This is a long-lasting solution without having short-term failures. This paper aims to design an ultra-thin cement concrete overlay using a developed critical stress model with sustainable concrete materials for low-volume roads.Design/methodology/approachIn this research paper, a parametric study was conducted using the ultra-thin concrete overlay finite element model developed with ANSYS software, considering the significant parameters affecting the performance and development. The non-linear regression equation was formed using a damped least-squares method to predict critical stress due to the corner load of 51 kN.FindingsThe parametric study results indicate that with a greater elastic modulus of bituminous concrete, granular layer along with 100 mm thickness of concrete layer reduces the critical corner stress, interface shear stress in a significant way responsible for debonding of concrete overlay, elastic strains in the pavement further the concrete overlay can bear infinite load repetitions. From validation, it is understood that the non-linear regression equation developed is acceptable with similar research work done.Originality/valueFrom the semi-scale experimental study, it is observed that the quaternary blended sustainable concrete overlay having a high modulus of rupture of 6.34 MPa is competent with conventional cement concrete overlay in terms of failure load. So, concrete overlay with sustainable materials of 100 mm thickness and higher elastic modulus of the layers can perform in a sustainable way meeting the environmental and long-term performance requirements.

An Improved Weighted Gradient Projection Method for Inverse Kinematics of Redundant Surgical Manipulators.

Different from traditional redundant manipulators, the redundant manipulators used in the surgical environment require the end effector (EE) to have high pose (position and orientation) accuracy to ensure the smooth progress of the operation. When analyzing the inverse kinematics (IK) of traditional redundant manipulators, gradient-projection method (GPM) and weighted least-norm (WLN) method are commonly used methods to avoid joint position limits. However, for the traditional GPM and WLN method, when joints are close to their limits, they stop moving, which greatly reduces the accuracy of the IK solution. When robotic manipulators enter a singular region, although traditional damped least-squares (DLS) algorithms are used to handle singularities effectively, motion errors of the EE will be introduced. Furthermore, selecting singular region through trial and error may cause some joint velocities exceed their corresponding limits. More importantly, traditional DLS algorithms cannot guide robotic manipulators away from singular regions. Inspired by the merits of GPM, WLN, and DLS methods, an improved weighted gradient projection method (IWGPM) is proposed to solve the IK problem of redundant manipulators used in the surgical environment with avoiding joint position limits and singularities. The weighted matrix of the WLN method and the damping factor of the DLS algorithm have been improved, and a joint limit repulsive potential field function and singular repulsive potential field function belong to the null space are introduced to completely keep joints away from the damping interval and redundant manipulators away from the unsafe region. To verify the validity of the proposed IWGPM, simulations on a 7 degree of freedom (DOF) redundant manipulator used in laparoscopic surgery indicate that the proposed method can not only achieve higher accuracy IK solution but also avoid joint position limits and singularities effectively by comparing them with the results of the traditional GPM and WLN method, respectively. Furthermore, based on the proposed IWGPM, simulation tests in two cases show that joint position limits have a great impact on the orientation accuracy, and singular potential energy function has a great impact on the position accuracy.

Convergence of Levenberg-Marquardt Estimates of Nonlinear Parameters in EIS Analysis of Coated Aluminum Panels

Equivalent circuit models are frequently employed to analyze electrochemical impedance spectroscopy (EIS) data. However, aside from some simple cases in which the equivalent circuit element parameters can be estimated directly from a plot of the data, the parameters for each of the equivalent circuit elements must often be estimated through the implementation of a nonlinear least-squares regression method. One frequently-used approach is the powerful Levenberg-Marquardt algorithm. This algorithm functions as a damped least-squares method that performs an interpolation between the steepest-descent and the Gauss-Newton methods for estimating nonlinear parameters. However, there are several challenges to using a Levenberg-Marquardt algorithm to model EIS data. The nonlinear nature of the impedance equations along with the difference in the magnitude of the parameter values can result in the algorithm failing to converge to a local minimum in the parameter space. This convergence challenge can be seen in determining equivalent circuit values for undamaged coating systems that have a high pore resistance, a small capacitance, as well as contributions from the underlying metal substrate. A Levenberg-Marquardt algorithm, along with a heuristic approach to use the raw data to improve the initial parameter estimates, is implemented that provides an improved approach for nonlinear regression fits of equivalent circuit models. A comparison of three equivalent circuit models fits, with residuals, for a two-layer coating system on an aluminum substrate is shown in the attached figure.Figure caption: Plot of EIS data (+ symbols) from a cured coating system prior to any environmental exposures compared with 3 equivalent circuit model fits (solid lines). The model fits were obtained using an NRL-developed Levenberg-Marquardt nonlinear regression fitting routine.The Department of Defense Strategic Environmental Research and Development Program (SERDP) sponsored this project under work unit 5399. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Office of Naval Research, the U.S. Navy, the Department of Defense, or the U.S. government. Figure 1

Inverse Kinematics of a 7-DOF Spraying Robot with 4R 3-DOF Non-spherical Wrist

In this paper, an Inverse Kinematics (IK) algorithm combining the analytical method and the numerical one is proposed to solve the IK problem of a 7-DOF spraying robot with 4R 3-DOF non-spherical wrist. Firstly, the 7-DOF spraying robot is transformed into a 7-DOF robot with 3R spherical wrist and the arm angle is used as the redundancy parameter. The approximate IK solution is calculated analytically using offset angle method by means of approximation. Secondly, the approximate solution is taken as the initial value of the iterative algorithm and by updating the joint angles through the damped least-square method with augmented Jacobian matrix, the final exact solution is obtained after a few iterations. Three simulation experiments show that the proposed algorithm not only has high computational efficiency and accuracy, but also can obtain multiple solutions and show the self-motion characteristics of the 7-DOF robot. The novel algorithm may be implemented in real-time control of the 7-DOF spraying robot.

A Modified DLS Scheme With Controlled Cyclic Solution for Inverse Kinematics in Redundant Robots

Redundancy in robotic manipulators has many advantages. It is successfully used to achieve better dexterity, and to avoid obstacles, singularities, or the kinematic limitations. However, redundancy makes the inverse kinematics (IK) problem harder to solve. The damped least squares (DLS) is a powerful method for calculating the IK of redundant robots, but it suffers from noncyclicity issue, where a closed curve motion in the Cartesian space of the end-effector (EEF) does not map into a closed curve in the joint space. This results in nonrepetitive motion in the joint space, even though the EEF motion is repetitive. In this article, we present a solution for the noncyclicity problem in the DLS method. The proposed scheme was successfully tested both in simulation (9 DoF robot) and on a real robotic manipulator (7 DoF robot).

Wireline Logs Constraint Borehole-to-Surface Resistivity Inversion Method and Water Injection Monitoring Analysis

Detection of the oil–water encroachment front is of great importance to water injection of oil reservoirs. In borehole-to-surface electrical imaging (BSEI), a high-power direct current is applied into a borehole through a well case and the electric potential on the surface, which is affected by the subsurface electrical change, is measured. However, further accurate interpretation of BSEI data is difficult due to the weak surface response, deep target layer, long inversion time, and uncertainty in unconstrained inversion. Therefore, a new method to enhance the surface response of the anomalous body and a new three-dimensional inversion approach based on the damped least-squares method are proposed. Simulation of the water injection and fracturing process was modeled in three dimensions using the finite difference method and the incomplete Cholesky conjugate gradient method. The inversion approach was applied by using the log data to construct a layered resistivity model and constrain the inversion. The forward modeling results suggest that the electric potential gradient can enhance the response of electrical variations in the target layer and help estimate the water injection direction, depending on the distance of electrical anomalies and the current source. In actual water injection monitoring, the BSEI inversion results suggest that layered resistivity model constrained three-dimensional inversion can improve the precision and accuracy of the resistivity inversion results and outline the water injection channeled to the adjacent wells.

Inverse kinematics solution and motion simulation of seven-degree-of-freedom ascending platform based on neural network

A pseudoinverse-based inverse kinetic solving scheme for 7-degree-of-freedom redundant aerial platform robotic arm, the scheme combines Minimum Velocity Norm scheme and damped least-square method, a close-loop damped minimum velocity norm scheme is set up which allows to avoid the joints’ limitation and to ensure the solution’s stability near the singularity position. Further, a genetic algorithm optimized BP neural network is built. Genetic algorithm can improve the training efficiency and avoid trapping in local optimal solution. The application of neural network can ensure the real-time of solution.

Three-Dimensional P-Wave Velocity Structure of Tehran from Local Micro-Earthquake Tomography

Tehran region is located at the southern foothills of central Alborz Mountains which is one of the most seismically active regions due to the convergence between the Arabian and the Eurasian plates. In this study, 3-D crustal velocity structure of Tehran region was investigated using first P-wave arrival times of events with magnitudes less than 4. Data used was recorded by the stations from Tehran Disaster Management and Mitigation Organization, Iranian Seismological Center and International Institute of Earthquake Engineering and Seismology from 2004 to 2018. In order to obtain the crustal velocity structure of Tehran, iterative, damped least-squares method was used to solve/obtain earthquake parameters and velocity structures, simultaneously. Final results show three tectonic characteristics in the study area including high velocity anomalies in northern and eastern Tehran Mountains, and low velocity anomaly in triangular Tehran basin, so that the separation of the eastern Tehran Mountains and Tehran basin is especially sharp in cross-section profiles. Moreover, some low velocity anomalies are appeared around major faults in the study area (e.g. North Tehran Fault). The tomographic maps also show that the Tehran region contains of an upper crust layer with the thickness of 6 km which is located over middle crust layer bedrock with constant velocity up to 15 km. This upper crust layer consists of a sedimentary layer (~ 3 km thickness) overlaid a basement layer. Moreover, the thick and thin upper crust layers are separated by North Tehran and Kosar/Ghasr-Firooz faultsystems from the Tehran basin, respectively.

Acceleration-level trajectory planning for a dual-arm space robot

In order to achieve disturbance rejection of the base while realizing the pre-capturing process under joint physical constraints (such as limited joint-angle, joint-velocity, joint-acceleration), this paper proposed an acceleration-level trajectory planning method for a dual-arm space robot. Firstly, the acceleration-level kinematic models are derived by using the velocity-level kinematics and linear and angular momentum conservation law. On this basis, the joint physical constraints are reformulated as a quadratic programming (QP) problem which can be converted to a piecewise-linear projection equation. Meanwhile, the improved damped least-squares (DLS) method is applied to design trajectory planning for the balance arm which is employed to keep the base disturbance free. Finally, simulation results verify the effectiveness of the proposed acceleration-level trajectory planning method.

Deeply-learnt damped least-squares (DL-DLS) method for inverse kinematics of snake-like robots

Recently, snake-like robots are proposed to assist experts during medical procedures on internal organs via natural orifices. Despite their well-spelt advantages, applications in radiosurgery is still hindered by absence of suitable designs required for spatial navigations within clustered and confined parts of human body, and inexistence of precise and fast inverse kinematics (IK) models. In this study, a deeply-learnt damped least squares method is proposed for solving IK of spatial snake-like robot. The robot’s model consists of several modules, and each module has a pair of serial-links connected with orthogonal twists. For precise control of the robot’s end-effector, damped least-squares approach is used to minimize error magnitude in a function modeled over analytical Jacobian of the robot. This is iteratively done until an apt joint vector needed to converge the robot to desired positions is obtained. For fast control and singularity avoidance, a deep network is built for prediction of unique damping factor required for each target point in the robot’s workspace. The deep network consists of 11 x 15 array of neurons at the hidden layer, and deeply-learnt with a huge dataset of 877,500 data points generated from workspace of the snake robot. Implementation results for both simulated and actual prototype of an eight-link model of the robot show the effectiveness of the proposed IK method. With error tolerance of 0.01 mm, the proposed method has a very high reachability measure of 91.59% and faster mean execution time of 9.20 (±16.92) ms for convergence. In addition, the method requires an average of 33.02 (±39.60) iterations to solve the IK problem. Hence, approximately 3.6 iterations can be executed in 1 ms. Evaluation against popularly used IK methods shows that the proposed method has very good performance in terms of accuracy and speed, simultaneously.

Identification of Linear and Nonlinear Parameters for Systems with Local Non-Linearity

A new method based on dynamic response sensitivity is proposed for the identification of local nonlinear system. The unknown local nonlinear hysteresis parameters are identified together with linear structural parameters. The sensitivities of structural dynamic response with respect to unknown parameters are derived. The identification equation is set up based on Taylor’s first order approximation, and is solved with the damped least-squares method. A four-story shearing system with rubber isolation bearing of nonlinear hysteresis model is studied to validate the proposed method. Numerical simulation with noisy measured accelerations shows that the proposed method can accurately identify both linear and nonlinear parameters of the system. This method provides a new approach for detecting local nonlinear structures with incomplete measured output information.

GA Based Adaptive Singularity-Robust Path Planning of Space Robot for On-Orbit Detection

As a new on-orbit detection platform, the space robot could ensure stable and reliable operation of spacecraft in complex space environments. The tracking accuracy of the space manipulator end-effector is crucial to the detection precision. In this paper, the Cartesian path planning method of velocity level inverse kinematics based on generalized Jacobian matrix (GJM) is proposed. The GJM will come across singularity issue in path planning, which leads to the infinite or incalculable joint velocity. To solve this issue, firstly, the singular value decomposition (SVD) is used for exposition of the singularity avoidance principle of the damped least squares (DLS) method. After that, the DLS method is improved by introducing an adaptive damping factor which changes with the singularity. Finally, in order to improve the tracking accuracy of the singularity-robust algorithm, the objective function is established, and two adaptive parameters are optimized by genetic algorithm (GA). The simulation of a 6-DOF free-floating space robot is carried out, and the results show that, compared with DLS method, the proposed method could improve the tracking accuracy of space manipulator end-effector.

Time-lapse seismic tomography of an underground mining zone

In this study, we determined P-wave tomographic images of the Yongshaba deposit, an underground mining zone in Guizhou Province, China, by inverting arrival-time data of micro-seismic events and blasts recorded by a passive seismic array consisting of 28 sensors during January to April 2014 using an event location technique and a travel-time tomography method that can handle complex seismic discontinuities. The damping parameter used in the damped least-squares method is determined with the help of trade-off curve. To reveal internal P-wave velocity changes of the study area under severe mining activities, a time-lapse data partition scheme is used. To assess the human influence on the underground structure, we introduce a parameter to measure the relative velocity changes in different periods. The resolution of the tomographic images and the robustness of the obtained features are examined by conducting a series of checkerboard resolution tests and a restoring resolution test. Our tomographic results obtained from the entire data set reveal a prominent low-velocity (low-V) zone and many obvious high-velocity (high-V) zones. These features match well with the geological setting and the excavation plan carried out in the mine, according to in-site surveys. The low-V zone may reflect empty volumes, stress releases and rock breaking and cracking caused by mining activities, whereas the high-V zones are probably the consequences of local stress concentrations caused by regional stress redistribution. The time-lapse tomographic images may reveal the process of stress concentrations caused by rock breaking due to the continuing excavations in the entire observation period, indicating that the mining activities influenced the rock property and caused complex changes of the underground structure.

A new prestack three-parameter amplitude variation with offset inversion method

Prestack seismic inversion is an important method in reservoir prediction and fluid identification. In this paper, we develop a new strategy to carry out a prestack three-parameter AVO inversion to obtain P-wave velocity, S-wave velocity, and density. Using the Aki and Richards equation to calculate the PP reflection coefficients, which is the approximation to the Zoeppritz PP equation, we re-derive the relationship between reflection coefficients and their partial derivatives with respect to P-wave velocity, S-wave velocity, and density. We transform the objective function into the form of matrix multiplication and solve it using a damped least-squares method and Tikhonov regularization method. Then we directly obtain the inversion results, including P-wave velocity, S-wave velocity and density. To demonstrate the validity of the proposed prestack inversion method, we set up a 1D forward simulation model and add uniform noise into the synthetic seismic records. Then we test the proposed method on the overthrust model and field data. In order to demonstrate its high accuracy and the efficiency of the Tikhonov regularization method, we carry out a damped least-squares inversion method using the same models as a comparison. We find that the proposed prestack seismic data AVO inversion method has higher anti-noise capability, accuracy, and efficiency, both in synthetic records and field data using the Tikhonov regularization method.

360° light field 3D display system based on a triplet lenses array and holographic functional screen

A 360° light field 3D display system is presented, which consists of a liquid crystal display, a novel triplet lenses array, and a holographic functional screen (HFS). The mapping relationship among pixels, 3D objects, and viewing positions are investigated. The aberration analysis of the single lens is carried out both in the simulation and the experiment, which shows that it cannot provide an excellent 3D image to the viewers. In order to suppress the aberrations, “the primary aberration theory” and “the damped least-squares method” are used for optical analysis and lens design. A 3D image with aberration correction can be viewed around the proposed display system.

Inverse Kinematics of a 7R 6-DOF Robot with Nonspherical Wrist Based on Transformation into the 6R Robot

The 7R 6-DOF robots with hollow nonspherical wrist have been proven more suitable for spray painting applications. However, the inverse kinematics of this kind of robot is still imperfect due to the coupling between position and orientation of the end-effector (EE). In this paper, a new and efficient algorithm for the inverse kinematics of a 7R 6-DOF robot is proposed. The proposed inverse kinematics algorithm is a two-step method. The geometry of the 7R 6-DOF robot is analyzed. A comparison between the 7R 6-DOF robot and the well-known equivalent 6R robot is made. Based on this comparison, a rational transformation between these two kinds of robots is constructed. Then the general inverse kinematics algorithm of the equivalent 6R robot is applied to calculate the approximate solutions of the 7R 6-DOF robot, in the first step. The Damped Least-Squares (DLS) method is employed to derive the exact solutions, in the second step. The accuracy and efficiency of the algorithm are tested on a 7R 6-DOF painting robot. The results show that the proposed algorithm is more advantageous in the case without an approximate solution, such as the initial point of a continuous trajectory.