Least-squares Optimization Method Research Articles

A Method for Solving LiDAR Waveform Decomposition Parameters Based on a Variable Projection Algorithm

Light detection and ranging (LiDAR) is commonly used to create high-resolution maps; however, the efficiency and convergence of parameter estimation are difficult. To address this issue, we evaluated the structural characteristics of received LiDAR signals by decomposing them into Gaussian functions and applied the variable projection algorithm of the separable nonlinear least-squares problem to the process of waveform fitting. First, using a variable projection algorithm, we separated the linear (amplitude) and nonlinear (center position and width) parameters in the Gaussian function model; the linear parameters are expressed with nonlinear parameters by the function. Thereafter, the optimal estimation of the characteristic parameters of the Gaussian function components was transformed into a least-squares problem only comprising nonlinear parameters. Finally, the Levenberg–Marquardt algorithm was used to solve these nonlinear parameters, whereas the linear parameters were calculated simultaneously in each iteration, and the estimation results satisfying the nonlinear least-square criterion were obtained. Five groups of waveform decomposition simulation data and ICESat/GLAS satellite LiDAR waveform data were used for the parameter estimation experiments. During the experiments, for the same accuracy, the separable nonlinear least-squares optimization method required fewer iterations and lesser calculation time than the traditional method of not separating parameters; the maximum number of iterations was reached before the traditional method converged to the optimal estimate. The method of separating variables only required 14 iterations to obtain the optimal estimate, reducing the computational time from 1128 s to 130 s. Therefore, the application of the separable nonlinear least-squares problem can improve the calculation efficiency and convergence speed of the parameter solution process. It can also provide a new method for parameter estimation in the Gaussian model for LiDAR waveform decomposition.

Improving the Quality of Magnetic Signature Reproduction by Increasing Flexibility of Multi-Dipole Model Structure and Enriching Measurement Information

The paper presents the construction of a multi-dipole model that allows reproducing magnetic signatures of ferromagnetic objects. The virtual object used in the paper is an ellipsoid, which is the source of synthetic data. To make the situation more realistic, noise is added to the synthetic data. Two significant improvements compared to previous work are presented. Three-axial magnetometers are introduced instead of uniaxial magnetometers. However, a more important change is the modification of the model structure that allows placing dipoles on the entire plane, e.g. object's deck. The multi-dipole model consists of an a priori assumed number of permanent and induced single-dipole models. Each single dipole is described by three magnetic moments and, depending on the applied approach, one or two dipole position parameters. The non-linear least-squares optimization method is used to determine model parameters. To assess the quality of magnetic signature reproduction, qualitative and quantitative forms are used. The final quality assessment is based on differences between the reference fields and the fields determined from the multi-dipole model. The applied modifications bring significant improvement, however, only their combined application allows to restore magnetic signatures with good quality for directions other than for which the data were available.

Study of long baseline optimization positioning algorithms Bbsed on redundancy measurement

Generally, underwater vehicles real-time navigation system works through the principle of spherical intersection. The number of array elements required for this method is fixed, but in the case of redundant array elements, they can't be fully utilized. This paper presents two optimization methods based on redundancy measurement. One approach is the steepest descent method and the other is Gauss-Newton method. The former searches for the minimum value of the measurement’s sum of squared residuals along the negative gradient direction, and the later, a non-linear least-squares optimization method that constantly revise regression coefficients through multiple iterations to minimize the sum of squared residuals. Simulation show that both methods are greatly affected by the initial position, the closer the distance between initial position to the target is, the smaller positioning error is. On the same initial position, the Gauss-Newton method has less positioning error than the steepest descent method. The conclusions have been proved to be valid by sea trial.

Assessment of landfill leachate in Nam Son, Hanoi using 3D electrical imaging and self-potential data

The main objective of this study was to assess the environmental impact of the Nam Son Landfill on the subsurface geological structure studied using 3D electrical imaging and self-potential investigations. The map of the equipotential was based on self-potential data and was indicative of concentrations of redox-active components, and the map of the electrical conductivity provided information about the mineralization of the groundwater. The electrical conductivity of the subsurface was obtained from 3D-electrical imaging analysis conducted using a Wenner-based array configuration. An inversion of the data was carried out using 3D regularized least-squares optimization methods with robust model constraints. Three profiles of 3D electrical imaging and 180 self-potential data points, scattered within the study area near the disposal site, were implemented. The self-potential method supports the results of the geoelectrical method relating to a contaminated zone in the survey area with a large negative self-potential anomaly of ∼−260 mV with respect to the reference of a contaminant plume. Interpretations of geophysical data showed a low resistivity zone (<10 Ω m), which appeared to be a fully saturated zone with leachate from the Nam Son open dumpsite. The correlation between geophysical investigations and hydrochemical analysis proved to show high conductivity zones related with landfill leachate.

Interfacial surface roughness determination by coherence scanning interferometry using noise compensation.

The capability of coherence scanning interferometry has been extended recently to include the determination of the interfacial surface roughness between a thin film and a substrate when the surface perturbations are less than ∼10 nm in magnitude. The technique relies on introducing a first-order approximation to the helical complex field (HCF) function. This approximation of the HCF function enables a least-squares optimization to be carried out in every pixel of the scanned area to determine the heights of the substrate and/or the film layers in a multilayer stack. The method is fast but its implementation assumes that the noise variance in the frequency domain is statistically the same over the scanned area of the sample. This results in reconstructed surfaces that contain statistical fluctuations. In this paper we present an alternative least-squares optimization method, which takes into account the distribution of the noise variance-covariance in the frequency domain. The method is tested using results from a simulator and these show a significant improvement in the quality of the reconstructed surfaces.

Design and Experimental Verification of Position-Dependent Passive Electromagnetic Damping

A linear dashpot is a common equipment used in shock and vibration isolation. It has been shown theoretically that the vibration isolation performance can be significantly improved by a damping profile that depends on the piston relative position. In this study, a position-dependent damping profile is realized by using electromagnetic principles. The idea is to have multiple coil windings on the outer cylinder and to use a magnet as a piston. The damping profile is tuned by changing the number of turns at each coil. As a result of the magnet-coil arrangement, the architecture also has the capability of being regenerative. A unique experimental setup is constructed that measures damping electrically in a multiple coil arrangement. Least-squares optimization method is used to tune the number of turns. It is shown that the coil turns can be successfully tailored to realize a desired damping profile. The position-dependent damping architecture has the potential to be used in future regenerative dampers.

Optimized Estimation of Surface Layer Characteristics from Profiling Measurements

New sampling techniques such as tethered-balloon-based measurements or small unmanned aerial vehicles are capable of providing multiple profiles of the Marine Atmospheric Surface Layer (MASL) in a short time period. It is desirable to obtain surface fluxes from these measurements, especially when direct flux measurements are difficult to obtain. The profiling data is different from the traditional mean profiles obtained at two or more fixed levels in the surface layer from which surface fluxes of momentum, sensible heat, and latent heat are derived based on Monin-Obukhov Similarity Theory (MOST). This research develops an improved method to derive surface fluxes and the corresponding MASL mean profiles of wind, temperature, and humidity with a least-squares optimization method using the profiling measurements. This approach allows the use of all available independent data. We use a weighted cost function based on the framework of MOST with the cost being optimized using a quasi-Newton method. This approach was applied to seven sets of data collected from the Monterey Bay. The derived fluxes and mean profiles show reasonable results. An empirical bias analysis is conducted using 1000 synthetic datasets to evaluate the robustness of the method.

Simulation of Water Temperature in a Small Pond Using Parametric Statistical Models: Implications of Climate Warming

AbstractChanges in temperature and precipitation patterns due to global warming are likely to affect the quantity and quality of water in different water bodies. Water temperature modeling techniques are usually employed to study the effects of global climate change on stream and river ecosystems. This study aims to identify a suitable air–water temperature relationship for a small aquatic pond in a semiarid region of India and examine the effects of increased water temperature on the small pond’s attributes. The performance of two parametric statistical models—simple linear regression (SLR) and four-parameter nonlinear logistic regression (NLR) models—was evaluated. The developed models were field tested for mean, minimum, and maximum air–water temperatures on daily, weekly, and monthly timescales. The model parameters were estimated from the measured air–water temperature time-series data using the least-squares optimization method. Model performance was evaluated using three statistical indicators—the ...

Error analysis of aspheric surface with reference datum.

Severe requirements of location tolerance provide new challenges for optical component measurement, evaluation, and manufacture. Form error, location error, and the relationship between form error and location error need to be analyzed together during error analysis of aspheric surface with reference datum. Based on the least-squares optimization method, we develop a least-squares local optimization method to evaluate form error of aspheric surface with reference datum, and then calculate the location error. According to the error analysis of a machined aspheric surface, the relationship between form error and location error is revealed, and the influence on the machining process is stated. In different radius and aperture of aspheric surface, the change laws are simulated by superimposing normally distributed random noise on an ideal surface. It establishes linkages between machining and error analysis, and provides an effective guideline for error correcting.

Kinetic modeling of polyurethane pyrolysis using non-isothermal thermogravimetric analysis

The pyrolysis of polyurethane was studied by dynamic thermogravimetry analysis (TGA). The studied polyurethane is used as organic binder in casting process to make sand cores and molds. A semi-empirical model is presented that can be used to describe polyurethane pyrolysis occurring during TGA experiments. This model assumes that the polyurethane is pyrolysed by several parallel independent reactions. The kinetic parameters of polyurethane pyrolysis were evaluated by fitting the model to the experimental data obtained by TGA over a wide variety of heating rates. A nonlinear least-squares optimization method is employed in the fitting procedure. A hybrid objectives based simultaneously on the mass (TG) and mass loss rate (DTG) curves has been used in the least-squares method. The values of the activation energy obtained by the non-linear fitting were then recalculated by the methods of Kissinger and Friedmand. Furthermore, the parameters obtained in the present paper were then compared with those reported in the literature.

COMPARISON OF LEVENBERG-MARQUARDT BASED LEAST SQUARES METHOD AND A HEURISTIC TECHNIQUE FOR ELECTRICITY DEMAND ESTIMATION

This paper focuses on demand estimation of electricity in Iran using artificial bee swarm optimization (ABSO) algorithm which is a recently invented metaheuristic technique. For this aim, two types of exponential and quadratic models are investigated to estimate the Iran’s electricity demand. These models are defined based on socio-economic indicators of population, gross domestic product (GDP), import and export figures. Owing to the fluctuations of the economic indicators and nonlinearity of the electricity demand, an efficient technique must be employed to find optimal or near optimal values of the models’ weighting factors. This paper proposes ABSO as an efficient approach for solving this problem. The available data of electricity demand in Iran from 1981 to 1999 is used for finding the optimal weighing factors and the data from 2000 to 2005 is used for testing the models. In order to evaluate the performance of the proposed methodology, the results are compared with the result obtained by the traditional nonlinear least-squares optimization method of and Levenberg–Marquardt (LM)

A measure theoretic approach to linear inverse atmospheric dispersion problems

Using measure theoretic arguments, we provide a general framework for describing and studying the general linear inverse dispersion problem where no a priori assumptions on the source function has been made (other than assuming that it is indeed a source, i.e. not a sink). We investigate the source-sensor relationship and rigorously state solvability conditions for when the inverse problem can be solved using a least-squares optimization method. That is, we derive conditions for when the least-squares problem is well-defined.

A GPU-accelerated and Monte Carlo-based intensity modulated proton therapy optimization system.

Conventional spot scanning intensity modulated proton therapy (IMPT) treatment planning systems (TPSs) optimize proton spot weights based on analytical dose calculations. These analytical dose calculations have been shown to have severe limitations in heterogeneous materials. Monte Carlo (MC) methods do not have these limitations; however, MC-based systems have been of limited clinical use due to the large number of beam spots in IMPT and the extremely long calculation time of traditional MC techniques. In this work, the authors present a clinically applicable IMPT TPS that utilizes a very fast MC calculation. An in-house graphics processing unit (GPU)-based MC dose calculation engine was employed to generate the dose influence map for each proton spot. With the MC generated influence map, a modified least-squares optimization method was used to achieve the desired dose volume histograms (DVHs). The intrinsic CT image resolution was adopted for voxelization in simulation and optimization to preserve spatial resolution. The optimizations were computed on a multi-GPU framework to mitigate the memory limitation issues for the large dose influence maps that resulted from maintaining the intrinsic CT resolution. The effects of tail cutoff and starting condition were studied and minimized in this work. For relatively large and complex three-field head and neck cases, i.e., >100,000 spots with a target volume of ∼ 1000 cm(3) and multiple surrounding critical structures, the optimization together with the initial MC dose influence map calculation was done in a clinically viable time frame (less than 30 min) on a GPU cluster consisting of 24 Nvidia GeForce GTX Titan cards. The in-house MC TPS plans were comparable to a commercial TPS plans based on DVH comparisons. A MC-based treatment planning system was developed. The treatment planning can be performed in a clinically viable time frame on a hardware system costing around 45,000 dollars. The fast calculation and optimization make the system easily expandable to robust and multicriteria optimization.

Variable Projection Method for Power System Modal Identification

Common power system disturbances are characterized by oscillations that either damp out, sustain or grow. This oscillatory response can be measured and analyzed to extract modal information of the system. In this paper we apply a nonlinear least-squares optimization method known as the variable projection method to power system models and data. The variable projection method is compared against several linear methods such as Prony analysis, Matrix-Pencil and ERA, and the results suggest the nonlinear least-squares approach is superior.

Moving source localization using seismic signal processing

Accurate localization of a seismic source in a near-field scenario where the distances between sensors and the source are less than a few wavelengths of the generated signal has shown to be a challenging task. Conventional localization algorithms often prove to be ineffective, as near-field seismic signals exhibit characteristics different from the well-studied far-field signals. The current work is aimed at the employment of a seismic sensor array for the localization and tracking of a near-field wideband moving source. In this paper, the mathematical derivation of a novel DOA estimation algorithm—dubbed the Modified Kirlin Method—has been presented in details. The estimated DOAs are then combined using a least-squares optimization method for source localization. The performance of the proposed method has been evaluated in a field experiment to track a moving truck. We also compare the DOA estimation and source localization results of the proposed method with those of two other existing methods originally developed for localization of a stationary wideband source; Covariance Matrix Analysis and the Surface Wave Analysis. Our results indicate that both the Surface Wave Analysis and the Modified Kirlin Methods are effective in locating and tracking a moving truck.

Application of HYDRUS 1D model for assessment of phenol–soil adsorption dynamics

Laboratory-scale batch, vertical, and horizontal column experiments were conducted to investigate the attenuative capacity of a fine-grained clayey soil of local origin in the surrounding of a steel plant wastewater discharge site in West Bengal, India, for removal of phenol. Linear, Langmuir, and Freundlich isotherm plots from batch experimental data revealed that Freundlich isotherm model was reasonably fitted (R (2) = 0.94). The breakthrough column experiments were also carried out with different soil bed heights (5, 10, and 15 cm) under uniform flow to study the hydraulic movements of phenol by evaluating time concentration flow behavior using bromide as a tracer. The horizontal migration test was also conducted in the laboratory using adsorptive phenol and nonreactive bromide tracer to explore the movement of solute in a horizontal distance. The hydrodynamic dispersion coefficients (D) in the vertical and horizontal directions in the soil were estimated using nonlinear least-square parameter optimization method in CXTFIT model. In addition, the equilibrium convection dispersion model in HYDRUS 1D was also examined to simulate the fate and transport of phenol in vertical and horizontal directions using Freundlich isotherm constants and estimated hydrodynamic parameters as input in the model. The model efficacy and validation were examined through statistical parameters such as the coefficient of determination (R (2)), root mean square error and design of index (d).

Bounding uncertainties in intrinsic human elimination half-lives and intake of polybrominated diphenyl ethers in the North American population

We examine the balance between intake, intrinsic elimination half-lives and human body burdens measured in biomonitoring for polybrominated diphenyl ethers (PBDEs) in the North American population using the population-level pharmacokinetic model developed by Ritter et al. (2011). Empirical data are collected from two studies that made total intake estimates for the North American population for the years 2004 and 2005, and eight biomonitoring studies for the years 1992 to 2009. We assume intake of PBDEs increased exponentially to a peak in 2004, and has since exponentially declined. The model is fitted to the empirical PBDE intake and biomonitoring data on PBDE body burden using a least-square optimization method by adjusting the intake in 2004 and 2038, and the intrinsic elimination rate constants, which can be expressed as equivalent half-lives. We fit the model in two types of scenarios using different combinations of PBDE intake estimates and biomonitoring data. Our modeling results indicate that there is an inconsistency between the PBDE intake estimates and the biomonitoring data, and that the inconsistency is likely due to underestimation of population-level intake. More efforts are needed to better characterize intake rates and identify potentially-unrecognized exposure pathways. Additional age-stratified biomonitoring data, and time trends of PBDE intakes would better constrain the model and provide an improved estimation of the intrinsic elimination half-lives.

Shafts Parameter Optimization Design for Lunar Rover Wheel-Leg Planetary Mechanism

Taking the wheel-legged lunar rover based on double-half-revolution mechanism as a research object, this paper has made a dynamics simulation for the simplified virtual prototype model of lunar rover under several typical road conditions, with the purpose of obtaining the mechanical data of the wheel-leg planetary mechanism shafts. On this basis, this paper established the finite element analysis model of the wheel-leg planetary mechanism shafts, and analyzed their stress by using finite element analysis software ANSYS. Based on ANSYS Parametric Design Language (APDL), the optimization design for the above shafts were done combined with the least-square approximation optimization method. The results show that the optimized shafts not only meet the strength requirement, but also their weights are about 30% lower than the original, which will provide a new and effective way for optimizing the whole wheel-leg structure of lunar rover.

Measurement-based Static Load Modeling Using the PMU data Installed on the University Load

Load modeling has a significant influence on power system analysis and control. In recent years, measurement-based load modeling has been widely practiced. In the load modeling algorithm, the model structure is determined and the parameters of the established model are estimated. For parameter estimation, least-squares optimization method is applied. The model parameters are estimated so that the error between the measured values and the predicted values is to be minimized. By introducing sliding window concept, on-line load modeling method can be performed which reflects the dynamic behaviors of loads in real-time. For the purpose of data acquisition, the measurement system including PMU is implemented in university level. In this paper, case studies are performed using real PMU data from Korea Univ. and Seoul National University of Science and Technology. The performances of modeling real and reactive power behaviors using exponential and ZIP load model are evaluated.

Closed-Loop Identification of Second-Order Plus Time Delay (SOPTD) Model of Multivariable Systems by Optimization Method

The closed-loop identification of second-order plus time delay (SOPTD) transfer function models of multivariable systems is presented based on optimization method using the combined step-up and step-down responses. The need for combined step up and step down changes in the set point is brought out for the convergence of the model parameters. A standard nonlinear least-squares optimization method is used to obtain the parameters of the SOPTD model transfer function matrix by minimizing the sum of squared errors between the closed-loop responses of the model and the actual process responses. A simple method is proposed to obtain the initial guess values of SOPTD transfer function model parameters from the main and interaction responses of the actual process. This method was applied to two-input two-output (TITO) second-order plus time delay (SOPTD), higher order and 3 × 3 SOPTD transfer function models of multivariable systems. The proposed method considerably reduces the computational time for the optimiza...