Nonlinear Least-squares Optimization Problem Research Articles

Initial-Pose Self-Calibration for Redundant Cable-Driven Parallel Robot Using Force Sensors Under Hybrid Joint-Space Control

This letter investigates initial-pose estimation (Cartesian position and orientation) for redundant cable-driven parallel robots (CDPRs). As the forward kinematics cannot be performed if the robot is equipped with incremental sensors, a calibration method using force sensors is proposed. The self-calibration problem is formulated as a non-linear least-squares optimization problem based on the hybrid joint-space control strategy. The redundant cables are tension-controlled; the other cables are maintained at a fixed length in the joint space. A position-determined cable adjustable force (P-CAF) performance index and the concept of calibratable space were proposed to maintain the quasi-static conditions. A simulated case study was used to validate the calibration process.

Graph Optimization Model Fusing BLE Ranging with Wi-Fi Fingerprint for Indoor Positioning.

To improve the user’s positioning accuracy of a Wi-Fi fingerprint-based positioning algorithm, this study proposes a graph optimization model based on the framework of o that fuses a Wi-Fi fingerprint and Bluetooth Low Energy (BLE) ranging technologies. In our model, the improvement in positioning can be formulated as a nonlinear least-squares optimization problem that a graph can represent. The graph regards users as nodes and our self-designed error functions between users as edges. In the graph, the nodes obtain the initial coordinates through Wi-Fi fingerprint positioning, and all error functions aggregate to a total error function to be solved. To improve the solution effect of the total error function and weaken the influence of measurement error, an information matrix, an edge selection principle, and a Huber kernel function are introduced. The Levenberg–Marquardt (LM) algorithm is used to solve the total error function and the affine transformation estimation is used for the drifting solution. Through experiments, the influence of the threshold in the Huber kernel function is explored, the relationship between the number of nodes in the graph and the optimization effect is analyzed, and the impact of the distribution of nodes is researched. The experimental results show improvements in the positioning accuracy of four common Wi-Fi fingerprint-matching algorithms: KNN, WKNN, GK, and Stg.

Point set registration for assembly feature pose estimation using simulated annealing nested Gauss-Newton optimization

PurposeThis paper aims to propose a fast and robust 3D point set registration method for pose estimation of assembly features with few distinctive local features in the manufacturing process.Design/methodology/approachThe distance between the two 3D objects is analytically approximated by the implicit representation of the target model. Specifically, the implicit B-spline surface is adopted as an interface to derive the distance metric. With the distance metric, the point set registration problem is formulated into an unconstrained nonlinear least-squares optimization problem. Simulated annealing nested Gauss-Newton method is designed to solve the non-convex problem. This integration of gradient-based optimization and heuristic searching strategy guarantees both global robustness and sufficient efficiency.FindingsThe proposed method improves the registration efficiency while maintaining high accuracy compared with several commonly used approaches. Convergence can be guaranteed even with critical initial poses or in partial overlapping conditions. The multiple flanges pose estimation experiment validates the effectiveness of the proposed method in real-world applications.Originality/valueThe proposed registration method is much more efficient because no feature estimation or point-wise correspondences update are performed. At each iteration of the Gauss–Newton optimization, the poses are updated in a singularity-free format without taking the derivatives of a bunch of scalar trigonometric functions. The advantage of the simulated annealing searching strategy is combined to improve global robustness. The implementation is relatively straightforward, which can be easily integrated to realize automatic pose estimation to guide the assembly process.

Cyclic Subcritical Water Injection into Bazhenov Oil Shale: Geochemical and Petrophysical Properties Evolution Due to Hydrothermal Exposure

In situ shale or kerogen oil production is a promising approach to developing vast oil shale resources and increasing world energy demand. In this study, cyclic subcritical water injection in oil shale was investigated in laboratory conditions as a method for in situ oil shale retorting. Fifteen non-extracted oil shale samples from Bazhenov Formation in Russia (98 °C and 23.5 MPa reservoir conditions) were hydrothermally treated at 350 °C and in a 25 MPa semi-open system during 50 h in the cyclic regime. The influence of the artificial maturation on geochemical parameters, elastic and microstructural properties was studied. Rock-Eval pyrolysis of non-extracted and extracted oil shale samples before and after hydrothermal exposure and SARA analysis were employed to analyze bitumen and kerogen transformation to mobile hydrocarbons and immobile char. X-ray computed microtomography (XMT) was performed to characterize the microstructural properties of pore space. The results demonstrated significant porosity, specific pore surface area increase, and the appearance of microfractures in organic-rich layers. Acoustic measurements were carried out to estimate the alteration of elastic properties due to hydrothermal treatment. Both Young’s modulus and Poisson’s ratio decreased due to kerogen transformation to heavy oil and bitumen, which remain trapped before further oil and gas generation, and expulsion occurs. Ultimately, a developed kinetic model was applied to match kerogen and bitumen transformation with liquid and gas hydrocarbons production. The nonlinear least-squares optimization problem was solved during the integration of the system of differential equations to match produced hydrocarbons with pyrolysis derived kerogen and bitumen decomposition.

Plane wave elastography: a frequency-domain ultrasound shear wave elastography approach

In this paper, we propose plane wave elastography (PWE), a novel ultrasound shear wave elastography (SWE) approach. Currently, commercial methods for SWE rely on directional filtering based on the prior knowledge of the wave propagation direction, to remove complicated wave patterns formed due to reflection and refraction. The result is a set of decomposed directional waves that are separately analyzed to construct shear modulus fields that are then combined through compounding. Instead, PWE relies on a rigorous representation of the wave propagation using the frequency-domain scalar wave equation to automatically select appropriate propagation directions and simultaneously reconstruct shear modulus fields. Specifically, assuming a homogeneous, isotropic, incompressible, linear-elastic medium, we represent the solution of the wave equation using a linear combination of plane waves propagating in arbitrary directions. Given this closed-form solution, we formulate the SWE problem as a nonlinear least-squares optimization problem which can be solved very efficiently. Through numerous phantom studies, we show that PWE can handle complicated waveforms without prior filtering and is competitive with state-of-the-art that requires prior filtering based on the knowledge of propagation directions.

Optimal models for estimating future infected cases of COVID-19 in Oman

The recent coronavirus disease 2019 (COVID-19) outbreak is of high importance in research topics due to its fast spreading and high rate of infections across the world. In this paper, we test certain optimal models of forecasting daily new cases of COVID-19 in Oman. It is based on solving a certain nonlinear least-squares optimization problem that determines some unknown parameters in fitting some mathematical models. We also consider extension to these models to predict the future number of infection cases in Oman. The modification technique introduces a simple ratio rate of changes in the daily infected cases. This average ratio is computed by employing the rule of Al-Baali [Numerical experience with a class of self-scaling quasi-Newton algorithms, JOTA, 96 (1998), pp. 533–553], in a sense to be defined, for measuring the infection changes.

Nonlinear breathing crack identification from time-domain sensitivity analysis

Breathing cracks are often encountered in engineering structures and detection of such cracks at the earliest stage is important for safety and serviceability of the structures. In this paper, a new breathing crack identification approach based on the time-domain sensitivity analysis is proposed. For the forward problem, the crack is simply treated as a nonlinear oscillator and how to model a structure with breathing cracks is specified. As regards the inverse crack identification, it is formulated as a nonlinear least-squares optimization problem and a new sensitivity-based approach is developed to get the solution. In doing so, the sensitivity analysis of the possibly non-differentiable breathing crack models is necessarily proceeded through a smoothing strategy. Moreover, to enhance the convergence, the trust-region constraint is introduced and the Tikhonov regularization is naturally called to tackle the constraint. Numerical examples are studied to verify the feasibility and efficiency of the proposed approach in breathing crack identification.

Data space reflectivity full waveform inversion

The full waveform inversion of seismic data aroused the hope to perform simultaneously and in automated way tomography and imaging by solving non-linear least-squares optimization problem. As it has been recognized early, brute force minimization by classical methods is hopeless if low time frequencies are absent in the data. The paper develops a reliable numerical technique for smooth velocity reconstruction via model space decomposition. We present realistic synthetic examples for validating presented algorithm.

Enabling Optimization-Based Localization for IoT Devices

In this paper, we propose an embedded optimization approach for the localization of Internet of Things (IoT) devices making use of range measurements from ultra-wideband (UWB) signals. Low-cost, low-power UWB radios provide time-of-arrival measurements with decimeter accuracy over large distances. UWB-based localization methods have been envisioned to enable feedback control in IoT applications, particularly, in GPS-denied environments, and large wireless sensor networks. In this paper, we formulate the localization task as a nonlinear least-squares optimization problem based on two-way time-of-arrival measurements between the IoT device and several UWB radios installed in a 3-D environment. For the practical implementation of large-scale IoT deployments we further assume only approximate knowledge of the UWB radio locations. We solve the resulting optimization problem directly on IoT devices equipped with off-the-shelf microcontrollers using state-of-the-art code generation techniques for plug-and-play deployment of the nonlinear-programming algorithms. This paper further provides practical implementation details to improve the localization accuracy for feedback control in experimental IoT applications. The experimental results finally show that subdecimeter localization accuracy can be achieved using the proposed optimization-based approach, even when the majority of the UWB radio locations are unknown.

Identification of an Airfoil-Store System with Cubic Nonlinearity via Enhanced Response Sensitivity Approach

This paper presents an investigation on parameters identification of an airfoil-store system with cubic nonlinearity via enhanced response sensitivity approach. The nonlinear aeroelastic behavior of the nonlinear airfoil system depends on the airfoil’s parameters, and thus the structural parameters of the airfoil should be identified accurately before aeroelastic analysis. The identification problem of the airfoil-store system is modeled as a nonlinear least-squares optimization problem. The enhanced response sensitivity approach has been recognized for parameter identification with time domain response data and is to be followed up in the present work. To do so, the autonomous vibration response of the nonlinear motion equation is obtained by the numerical integration, and then the response sensitivity with respect to the unknown parameters is calculated likewise. Numerical tests are performed to show the effectiveness, the convergence, the sensitivity to initial parameter values, and measurement noises of the present approach in the airfoil-store system.

Cuckoo Search Algorithm with Lévy Flights for Global-Support Parametric Surface Approximation in Reverse Engineering

This paper concerns several important topics of the Symmetry journal, namely, computer-aided design, computational geometry, computer graphics, visualization, and pattern recognition. We also take advantage of the symmetric structure of the tensor-product surfaces, where the parametric variables u and v play a symmetric role in shape reconstruction. In this paper we address the general problem of global-support parametric surface approximation from clouds of data points for reverse engineering applications. Given a set of measured data points, the approximation is formulated as a nonlinear continuous least-squares optimization problem. Then, a recent metaheuristics called Cuckoo Search Algorithm (CSA) is applied to compute all relevant free variables of this minimization problem (namely, the data parameters and the surface poles). The method includes the iterative generation of new solutions by using the Lévy flights to promote the diversity of solutions and prevent stagnation. A critical advantage of this method is its simplicity: the CSA requires only two parameters, many fewer than any other metaheuristic approach, so the parameter tuning becomes a very easy task. The method is also simple to understand and easy to implement. Our approach has been applied to a benchmark of three illustrative sets of noisy data points corresponding to surfaces exhibiting several challenging features. Our experimental results show that the method performs very well even for the cases of noisy and unorganized data points. Therefore, the method can be directly used for real-world applications for reverse engineering without further pre/post-processing. Comparative work with the most classical mathematical techniques for this problem as well as a recent modification of the CSA called Improved CSA (ICSA) is also reported. Two nonparametric statistical tests show that our method outperforms the classical mathematical techniques and provides equivalent results to ICSA for all instances in our benchmark.

ORB-SHOT SLAM: Trajectory Correction by 3D Loop Closing Based on Bag-of-Visual-Words (BoVW) Model for RGB-D Visual SLAM

[abstFig src='/00290002/10.jpg' width='300' text='Visual odometry + trajectory correction' ] This paper proposes the ORB-SHOT SLAM or OS-SLAM, which is a novel method of 3D loop closing for trajectory correction of RGB-D visual SLAM. We obtain point clouds from RGB-D sensors such as Kinect or Xtion, and we use 3D SHOT descriptors to describe the ORB corners. Then, we train an offline 3D vocabulary that contains more than 600,000 words by using two million 3D descriptors based on a large number of images from a public dataset provided by TUM. We convert new images to bag-of-visual-words (BoVW) vectors and push these vectors into an incremental database. We query the database for new images to detect the corresponding 3D loop candidates, and compute similarity scores between the new image and each corresponding 3D loop candidate. After detecting 2D loop closures using ORB-SLAM2 system, we accept those loop closures that are also included in the 3D loop candidates, and we assign them corresponding weights according to the scores stored previously. In the final graph-based optimization, we create edges with different weights for loop closures and correct the trajectory by solving a nonlinear least-squares optimization problem. We compare our results with several state-of-the-art systems such as ORB-SLAM2 and RGB-D SLAM by using the TUM public RGB-D dataset. We find that accurate loop closures and suitable weights reduce the error on trajectory estimation more effectively than other systems. The performance of ORB-SHOT SLAM is demonstrated by 3D reconstruction application.

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

Abstract. We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection–diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations and model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov–Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems – i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian – we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. We show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.

Fokker–Planck linearization for non-Gaussian stochastic elastoplastic finite elements

Presented here is a finite element framework for the solution of stochastic elastoplastic boundary value problems with non-Gaussian parametric uncertainty. The framework relies upon a stochastic Galerkin formulation, where the stiffness random field is decomposed using a multidimensional polynomial chaos expansion. At the constitutive level, a Fokker–Planck–Kolmogorov (FPK) plasticity framework is utilized, under the assumption of small strain kinematics. A linearization procedure is developed that serves to update the polynomial chaos coefficients of the expanded random stiffness in the elastoplastic regime, leading to a nonlinear least-squares optimization problem. The proposed framework is illustrated in a static shear beam example of elastic-perfectly plastic as well as isotropic hardening material.

Modified Gauss-Newton full-waveform inversion explained — Why sparsity-promoting updates do matter

Full-waveform inversion (FWI) can be formulated as a nonlinear least-squares optimization problem. This nonconvex problem can be computationally expensive because it requires repeated solutions of the wave equation. Randomized subsampling techniques allow us to work with small subsets of (monochromatic) source experiments, reducing the computational cost. However, this subsampling may weaken subsurface illumination or introduce subsampling-related incoherent artifacts. These subsampling-related artifacts — in conjunction with the desire to obtain high-fidelity inversion results — motivate us to come up with a technique to regularize this inversion problem. Following earlier work, we have taken advantage of the fact that curvelets represent subsurface models and model perturbations parsimoniously. At first impulse, promoting sparsity on the model directly seemed the most natural way to proceed, but we have determined that in certain cases it can be advantageous to promote sparsity on the Gauss-Newton updates instead. Although constraining the one norm of the descent directions did not change the underlying FWI objective, the constrained model updates remained descent directions, removed subsampling-related artifacts, and improved the overall inversion result. We have empirically observed this phenomenon in situations where the different model updates occurred at roughly the same locations in the curvelet domain. We have further investigated and analyzed this behavior, in which nonlinear inversions benefit from sparsity-promoting constraints on the updates, by means of a set of carefully selected examples including the phase retrieval problem and time-harmonic FWI. In all cases, we have observed a faster decay of the residual and model error as a function of the number of iterations.

Achieving Target Emulsion Drop Size Distributions Using Population Balance Equation Models of High-Pressure Homogenization

Population balance equation (PBE) models have been used extensively to predict drop size distributions (DSDs) of dispersed phase systems. In our previous publications, we have used the PBE framework to develop increasingly sophisticated process models for oil-in-water emulsification in high-pressure homogenizers. The goal of this study was to utilize these PBE models for integrated emulsion product and process design through the formulation and solution of homogenizer optimization problems. For a specified number of homogenization passes, the initial amount of surfactant and the pressure of each pass were determined by solving a nonlinear least-squares optimization problem such that the target DSD were achieved. Three alternative objective functions that differed with respect to the distribution specification and the penalty on surfactant usage were formulated and solved for different target DSDs. The model predictions were successfully validated by performing homogenization experiments using the optimized formulation and homogenization variables.

Stabilization of projection-based reduced order models for linear time-invariant systems via optimization-based eigenvalue reassignment

A new approach for stabilizing unstable reduced order models (ROMs) for linear time-invariant (LTI) systems through an a posteriori post-processing step applied to the algebraic ROM system is developed. The key idea is to modify the unstable eigenvalues of the ROM system by moving these eigenvalues into the stable half of the complex plane. It is demonstrated that this modification to the ROM system eigenvalues can be accomplished using full state feedback (a.k.a. pole placement) algorithms from control theory. This approach ensures that the modified ROM is stable provided the system’s unstable poles are controllable and observable; however, the accuracy of the stabilized ROM is not guaranteed. To remedy this difficulty and guarantee an accurate stabilized ROM, a constrained nonlinear least-squares optimization problem for the stabilized ROM eigenvalues in which the error in the ROM output is minimized is formulated. This optimization problem is small and therefore computationally inexpensive to solve. Performance of the proposed algorithms is evaluated on two test cases for which ROMs constructed via the proper orthogonal decomposition (POD)/Galerkin method suffer from instabilities.

Firefly Algorithm for Explicit B-Spline Curve Fitting to Data Points

This paper introduces a new method to compute the approximating explicit B-spline curve to a given set of noisy data points. The proposed method computes all parameters of the B-spline fitting curve of a given order. This requires to solve a difficult continuous, multimodal, and multivariate nonlinear least-squares optimization problem. In our approach, this optimization problem is solved by applying the firefly algorithm, a powerful metaheuristic nature-inspired algorithm well suited for optimization. The method has been applied to three illustrative real-world engineering examples from different fields. Our experimental results show that the presented method performs very well, being able to fit the data points with a high degree of accuracy. Furthermore, our scheme outperforms some popular previous approaches in terms of different fitting error criteria.

An inexact Gauss-Newton method for inversion of basal sliding and rheology parameters in a nonlinear Stokes ice sheet model

AbstractWe propose an infinite-dimensional adjoint-based inexact Gauss-Newton method for the solution of inverse problems governed by Stokes models of ice sheet flow with nonlinear rheology and sliding law. The method is applied to infer the basal sliding coefficient and the rheological exponent parameter fields from surface velocities. The inverse problem is formulated as a nonlinear least-squares optimization problem whose cost functional is the misfit between surface velocity observations and model predictions. A Tikhonov regularization term is added to the cost functional to render the problem well-posed and account for observational error. Our findings show that the inexact Newton method is significantly more efficient than the nonlinear conjugate gradient method and that the number of Stokes solutions required to solve the inverse problem is insensitive to the number of inversion parameters. The results also show that the reconstructions of the basal sliding coefficient converge to the exact sliding coefficient as the observation error (here, the noise added to synthetic observations) decreases, and that a nonlinear rheology makes the reconstruction of the basal sliding coefficient more difficult. For the inversion of the rheology exponent field, we find that horizontally constant or smoothly varying parameter fields can be reconstructed satisfactorily from noisy observations.

Parameter sensitivity analysis of a nonlinear least-squares optimization-based anelastic full waveform inversion method

In a recent article, we described a seismic inversion method for determining the crustal velocity and attenuation of basins in earthquake-prone regions. We formulated the problem as a constrained nonlinear least-squares optimization problem in which the constraints are the equations that describe the forward wave propagation. Here, we conduct a parametric study to investigate the influence of parameters such as the form of the regularization function, receiver density, preconditioning, noise level of the data, and the multilevel continuation technique on the cost and quality of the inversion. We use the same 2D Los Angeles example as in our earlier study.