Nonlinear Optimization Approach Research Articles

Enhancing ocean color retrieval in sunglint regions: the efficacy of IPNOA over conventional atmospheric correction methods

Sunglint significantly impacts the extraction of ocean color information, particularly for sensors lacking tilt capabilities. Traditional atmospheric correction algorithms often fail to retrieve effective data in high-sunglint regions. The polynomial-based POLYMER method, applied to MERIS data, effectively addresses sunglint, although its accuracy decreases by about 15% in such conditions. To enhance data reliability in sunglint regions, we propose the Improved polynomial nonlinear optimization approach (IPNOA), a revision of the POLYMER atmospheric correction. IPNOA employs the QAA-RGR (quasi-analytical algorithm-red-green-bands-ratio) to refine the bio-optical ocean reflectance model. Additionally, due to the nonlinear optimization algorithm’s sensitivity to initial values, this study uses global 8-day average oceanic optical properties at 4 km resolution as the initial setting. The performance of IPNOA was initially evaluated using a synthetic dataset, with retrieved remote sensing reflectance (Rrs) closely matching the simulated Rrs across all wavelengths. The mean absolute percentage error (MAPE) remained below 1% for non-sunglint, moderate sunglint, and high sunglint conditions. Further analysis of in situ data revealed that IPNOA performs better, exceptionally at 412 nm, with a MAPE of 5.27% in sunglint regions. When processed by POLYMER, the dataset exhibited a MAPE of 68.47%. Finally, an analysis of global data from MODIS, VIIRS, and HY1C/D on July 15, 2022, showed good agreement among the three on a global scale. Above all, these results indicate that the IPNOA algorithm has strong potential for retrieving valid products in moderate, even high sunglint regions, offering practical benefits for expanding the spatial coverage of ocean color satellite data.

A nonlinear optimal control approach for dual-arm robotic manipulators

A nonlinear optimal control approach for dual-arm robotic manipulators

Automated parking trajectory planning: a hybrid curve search and nonlinear optimisation approach

ABSTRACT This paper focuses on the problem of automatic parking trajectory planning in unstructured scenarios. The proposed algorithm adopts a combination of graph search and optimization strategy. First, A* search is utilized to obtain paths connecting the global start and end points. Second, the path is divided into three segments and subpaths are searched using the hybrid A* algorithm and the proposed A*-iBspline algorithm. Finally, the three subpaths are merged and a valid initial guess is generated for the OCP. Additionally, an iterative framework is used to improve the quality of the OCP solution. Simulation results show that the proposed algorithm has a significant advantage over existing methods in terms of time and applicability.

A nonlinear optimal control approach for 3-DOF four-cable driven parallel robots

In this article, a nonlinear optimal control approach is proposed for the dynamic model of 3-DOF four-cable driven parallel robots (CDPR). To solve the associated nonlinear optimal control problem, the dynamic model of the 3-DOF cable-driven parallel robot undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the 3-DOF cable-driven parallel robot a stabilizing optimal (H-infinity) feedback controller is designed. To compute the controller’s feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. The proposed nonlinear optimal control approach achieves fast and accurate tracking of reference setpoints under moderate variations of the control inputs and a minimum dispersion of energy.

Enhancing DC distribution network efficiency through optimal power coordination in lithium-ion batteries: A sparse nonlinear optimization approach

This work deals with the problem regarding the optimal operation of lithium-ion batteries to improve the economic, technical, and environmental indices of standalone and grid-connected direct current (DC) distribution networks.To this effect, a general nonlinear programming model has been developed, which considers three objective functions: (i) the daily energy purchasing costs at the terminals of the substation, considering the maintenance costs of renewable generation (photovoltaic) and energy storage technologies (batteries); (ii) the daily energy losses associated with energy transport; and (iii) the CO2 emissions per day of operation, associated with conventional generators. This is done by integrating all the operations and technical constraints of the DC network and the devices it comprises. The sparse nonlinear optimization (SNOPT) solution method is employed, comparing its results against those of three recently reported metaheuristic optimization methodologies: the continuous genetic algorithm and the parallel versions of the particle swarm optimizer and the vortex search algorithm. The performance of the proposed methodology is validated on standalone and grid-connected networks, considering the technical and economic conditions of two regions of Colombia (rural and urban territories) and evaluating its effectiveness in terms of solution quality, standard deviation, and processing times. The results show that the SNOPT tool of the General Algebraic Modeling System (GAMS) achieves the global optimum in all test scenarios, exhibiting a standard deviation of zero and requiring less than three seconds on average to generate a solution for an entire day of operation.

Independent component analysis and finite element modelling of the 2004–2005 ground deformation in Tenerife (Canary Islands)

Historic volcanic activity in Tenerife was concentrated within two of the island’s three dorsals and on the Teide-Pico Viejo complex located inside Las Cañadas caldera. Eruptions on the island are primarily characterised by basaltic and trachybasaltic fissural eruptions. However, the Teide-Pico Viejo complex also hosted explosive and effusive phonolitic eruptions. Our study focused on the analysis of the 2004–2005 unrest in Tenerife, which was characterised by an onset of a ground deformation pattern, heightened on-land seismic activity, changes in the chemical composition of fumaroles of the Teide composite volcano, an increase in diffusive emissions of carbon dioxide along the NW rift, and, significant gravity changes. We used the Envisat-ASAR satellite images from 2003 to 2010 to generate the Line-Of-Sight SBAS-DInSAR deformation time series to investigate the source responsible for ground deformation. We applied the Independent Component Analysis (ICA) to separate distinct ground deformation patterns. Specifically, we selected four components for the Independent Component Analysis decomposition: the first one mainly affects the stratovolcano’s summit region of Teide and shows a circular symmetry; the second and third components are possibly related to the topography and atmospheric artifacts, while the fourth contains only a noisy signal. We employed a non-linear optimisation approach in a Finite Element modelling environment to determine the source geometry responsible for the first identified ICA pattern of ground deformation within Las Cañadas. Our results revealed the existence of an ellipsoidal ground deformation source oriented along the E-W axis, located beneath the Teide and Montaña Blanca volcanoes at 1,600 m a.s.l. This source became active during the seismic crisis of 2004–2005, which was associated with the degassing of a magma batch that intruded into the northwest rift of Tenerife island. We propose that the ground deformation observed at Teide volcano during the 2004–2005 crisis was related to hydrothermal activity within the volcano.

Nonlinear optimal control for triangular tethered multi-satellite formations

Triangular satellite constellations are created by three satellites which are linked through tethers. Such formations serve distributed observation space missions or the creation of high-density satellite communication networks over high-frequency bands. In a tethered multi-satellite system consisting of three-satellites in triangular formation the associated dynamic model exhibits strong nonlinearities. Stabilization and precise positioning of the multi-satellite constellation is a nontrivial task and the solution of the associated nonlinear control problem is an elaborated procedure. In this article a novel nonlinear optimal control method is applied to the above-noted model the tethered multi-satellite system in triangular formation. First, the state-space model of the triangular tethered multi-satellite formation undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the tethered satellites a stabilizing optimal (H-infinity) feedback controller is designed. This controller stands for the solution of the nonlinear optimal control problem under model uncertainty and external perturbations. To compute the controller’s feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. The proposed nonlinear optimal control approach achieves fast and accurate tracking of setpoints under moderate variations of the control inputs and a minimum dispersion of energy when changing the position of the satellites in their triangular tethered formation.

Wasserstein-penalized Entropy closure: A use case for stochastic particle methods

We introduce a framework for generating samples of a distribution given a finite number of its moments, targeted at particle-based solutions of kinetic equations and rarefied gas flow simulations. Our model, referred to as the Wasserstein-Entropy distribution (WE), couples a physically-motivated Wasserstein penalty term to the traditional maximum-entropy distribution (MED) function, which serves to regularize the latter. The penalty term becomes negligible near the local equilibrium, reducing the proposed model to the MED, known to reproduce the hydrodynamic limit. However, in contrast to the standard MED, the proposed WE closure can cover the entire physically realizable moment space, including the so-called Junk line. We also propose an efficient Monte Carlo algorithm for generating samples of the unknown distribution which is expected to outperform traditional non-linear optimization approaches used to solve the MED problem. Numerical tests demonstrate that given moments up to the heat flux—that is, information equivalent to that contained in the Chapman-Enskog distribution—the proposed methodology provides a reliable closure in the collision-dominated and early transition regimes. Applications to greater rarefaction demand information from higher-order moments, which can be incorporated within the proposed closure.

Generalized geometric pore size distribution code GPSD-3D for periodic systems composed of monodisperse spheres

The generalized geometric pore size distribution P(r;rp|rc) as function of pore radius r, probe sphere radius rp, and coating thickness rc for a periodic two-dimensional system composed of circles (GPSD-2D) had been defined recently. For rp=rc=0 it reduces to the widely accepted pore radius distribution P(r) introduced by Gelb and Gubbins. The three-dimensional counterpart GPSD-3D for periodic systems composed of spheres is implemented here using an efficient Voronoi-based semi-analytic strategy that offers significant advantages compared with both a grid-based implementation and constrained nonlinear optimization with respect to speed, precision and memory requirements. Moreover, GPSD-3D is fully parallelized using OpenMP. Program summaryProgram title:GPSD-3DCPC library link to program files:https://doi.org/10.17632/ntcr87fgr5.1Developers repository link:https://github.com/mkmat/CODE-GPSD-3DLicensing provisions: MITProgramming languages:fortran, c++, perlNature of problem: Calculation of a set of pore radii for a user-provided configuration of (material) spheres contained in a periodic three-dimensional, rectangular box. This set depends on the user-specified radius rp of a probe sphere, and a user-specified hypothetical coating thickness rc of the material spheres. The variable size of the set, and thus the resolution of the resulting generalized geometric pore size distribution increases linearly with computing time.Solution method: Analytic calculation of pore radii from the Voronoi faces for the case of monodisperse systems, constrained nonlinear optimization or grid-based approach for polydisperse systems.Additional comments: This code requires a c++ compiler such as g++, a OpenMP-supporting fortran compiler such as gfortran, perl, and the voro++ library. Download links will be automatically provided during installation of GPSD-3D.

MiPhDUO: microwave imaging via physics-informed deep unrolled optimization

Microwave imaging (MWI) is a non-invasive technique that can identify unknown scatterer objects’ features while offering advantages such as low cost and portable devices with respect to other imaging methods. However, MWI faces challenges in solving the underlying inverse scattering problem, which involves recovering target properties from its scattered fields. Existing methods include linearized and non-linear optimization approaches, but they have limitations respectively in terms of range of validity and computational complexity (in view of the possible occurrence of ‘false solutions’). In recent years, learning-based approaches have emerged as they can allow real-time imaging but usually lack generalizability and a direct connection to the underlying physics. This paper proposes a physics-informed approach that combines convolutional neural networks with physics-based calculations. It is based on a few cascaded operations, making use of the gradient of the relevant cost function, and successively improving the estimation of the unknown target. The proposed approach is assessed using simulated as well as experimental Fresnel data. The results show that the integration of physics with deep learning can contribute to improve reconstruction accuracy, generalizability, and computational efficiency in MWI.

Two-frame wavefront reconstruction method with nonlinear optimization for Ronchi lateral shearing interferometry

Ronchi lateral shearing interferometry is widely applied in wavefront measurement of advanced lithography tools. In Ronchi lateral shearing interferometry, higher-order diffraction beam interference is a common challenge, currently mitigated by introducing more phase shifts, resulting in extended measurement times and added errors. In this study, we propose a nonlinear optimization approach that combines a 2-frame phase-shifting algorithm to suppress the influence of high diffraction orders, reducing the required number of phase shifts by more than 75%. We formulate a numerical model that aligns with the interferometry, construct a highly robust error function, and enable high-precision wavefront reconstruction by optimizing Zernike coefficients. The accuracy and robustness of the proposed method are verified through simulations and experiments.

Toward Interpretable-AI Policies Using Evolutionary Nonlinear Decision Trees for Discrete-Action Systems.

Black-box artificial intelligence (AI) induction methods such as deep reinforcement learning (DRL) are increasingly being used to find optimal policies for a given control task. Although policies represented using a black-box AI are capable of efficiently executing the underlying control task and achieving optimal closed-loop performance-controlling the agent from the initial time step until the successful termination of an episode, the developed control rules are often complex and neither interpretable nor explainable. In this article, we use a recently proposed nonlinear decision-tree (NLDT) approach to find a hierarchical set of control rules in an attempt to maximize the open-loop performance for approximating and explaining the pretrained black-box DRL (oracle) agent using the labeled state-action dataset. Recent advances in nonlinear optimization approaches using evolutionary computation facilitate finding a hierarchical set of nonlinear control rules as a function of state variables using a computationally fast bilevel optimization procedure at each node of the proposed NLDT. In addition, we propose a reoptimization procedure for enhancing the closed-loop performance of an already derived NLDT. We evaluate our proposed methodologies (open- and closed-loop NLDTs) on different control problems having multiple discrete actions. In all these problems, our proposed approach is able to find relatively simple and interpretable rules involving one to four nonlinear terms per rule, while simultaneously achieving on par closed-loop performance when compared to a trained black-box DRL agent. A postprocessing approach for simplifying the NLDT is also suggested. The obtained results are inspiring as they suggest the replacement of complicated black-box DRL policies involving thousands of parameters (making them noninterpretable) with relatively simple interpretable policies. The results are encouraging and motivating to pursue further applications of proposed approach in solving more complex control tasks.

A nonlinear optimal control approach for unmanned surface vessels

A nonlinear optimal control approach for unmanned surface vessels

Surface profile measurement using nonlinear optimization approach in diffraction phase microscopy

Nanoscale measurement of surface profile has important application in the field of non-destructive surface testing and evaluation. We propose a nonlinear optimization based phase retrieval approach in diffraction phase microscopy for nanoscale surface profile measurement. The proposed approach relies on minimizing an objective function derived from the interferogram signal and the application of total variation regularization. The performance of the method is demonstrated via numerical simulations for processing interferograms affected by sharp phase variations, noise and non-uniform amplitude fluctuations. In addition, the practical application of the method is validated for nanoscale surface topography by processing experimental interferograms obtained in diffraction phase microscopy.

Tailored Dispersion and Nonlinear Effects in Flint Glass Honeycomb PCF for Optical Communication

This paper describes a highly nonlinear flint glass-based honeycomb photonic crystal fiber (FGH-PCF) with a wavelength of 1550 nm. The PCF’s distinctive honeycomb lattice structure, combined with the nonlinear capabilities of flint glass, enables a wide range of nonlinear optical applications. To adjust the PCF's dispersion and nonlinear effects, numerical simulations and optimization approaches were used. To achieve maximum performance, fabrication procedures were carefully regulated. Dispersion values of −436.6 ps/(nm.km) for x polarization and −448.1 ps/(nm.km) for y polarization were verified by experimental characterization. The PCF displayed low confinement losses of 2.289 dB/cm (x polarization) and 4.935 dB/cm (y polarization), as well as birefringence of 2.202×10-3. The PCF measured 558.8 and 547.9 W-1 km-1 for x and y polarization, respectively, indicating a high nonlinear coefficient. The highly nonlinear FGH-PCF shows promising potential for nonlinear optical applications such as four-wave mixing, supercontinuum generation, frequency conversion, and parametric amplification. This research paves the way for compact and efficient nonlinear devices in modern optical communication systems and other cutting-edge technologies.

A zeroing neural network model for form-finding problems: A nonlinear optimization approach

How to establish a simple and efficient nonlinear optimization problem form-finding model in noise environments is the main concern of this paper, thereby, a sequential quadratic programming form-finding (SQP) approach via a noise-tolerant zeroing neural network (NTZNN) is presented to solve the proposed problem. First, the rank of force density matrix is selected as optimization objective due to its crucial physical property. In addition, linear relations between the force density vectors and force density matrix are selected as the constraint conditions, which can ensure the tensegrity mechanism in a stable status. Furthermore, the simulations are shown that the presented SQP-NTZNN algorithm has superiority with anti-noise performance and computation efficiency, which by comparing the computational rate in the same noise environment with the novel form-finding algorithm. Eventually, the form-finding simulations under different initial conditions are formed to verify the importance of the constrained conditions, it can prove the high efficiency of the proposed nonlinear constrained optimization model which is transformed from the form-finding problem.

A robust state-dependent Riccati equation controller with parameter uncertainty and matched disturbance

The state-dependent Riccati equation (SDRE) unveils a nonlinear optimal control approach; the method is sensitive to uncertainty and disturbance that provokes the necessity of precise modeling and omitting disturbance from the model and environment which is occasionally impossible. In this paper, a robust state-dependent Riccati equation is introduced using only the pure SDRE itself. Lyapunov’s second method for stability analysis is used to extract two tuning rules for weighting matrices of the robust approach for handling both matched disturbance and parametric uncertainty. A fourth-order differential equation is simulated to show the effectiveness of the suggested method and the results were compared with conventional SDRE. The robust version could handle the matched disturbance with a steady-state shift from the equilibrium point where the conventional SDRE failed. Additionally, a comparison and detailed analysis have been performed between the proposed design and sliding mode control.

Using the Orthogonal Conditional Nonlinear Optimal Perturbations Approach to Address the Uncertainties of Tropical Cyclone Track Forecasts Generated by the WRF Model

Abstract The orthogonal conditional nonlinear optimal perturbations (O-CNOPs) approach for measuring initial uncertainties is applied to the Weather Research and Forecasting (WRF) Model to provide skillful forecasts of tropical cyclone (TC) tracks. The hindcasts for 10 TCs selected from 2005 to 2020 show that the ensembles generated by the O-CNOPs have a greater probability of capturing the true TC tracks, and the corresponding ensemble forecasts significantly outperform the forecasts made by the singular vectors, bred vectors, and random perturbations in terms of both deterministic and probabilistic skills. In particular, for two unusual TCs, Megi (2010) and Tembin (2012), the ensembles generated by the O-CNOPs successfully reproduce the sharp northward-turning track in the former and the counterclockwise loop track in the latter, while the ensembles generated by the other methods fail to do so. Moreover, additional attempts are performed on the real-time forecasts of TCs In-Fa (2021) and Hinnamnor (2022), and it is shown that O-CNOPs are very useful for improving the accuracy of real-time TC track forecasts. Therefore, O-CNOPs, together with the WRF Model, could provide a new platform for the ensemble forecasting of TC tracks with much higher skill.

Nonlinear optimal control for permanent magnet synchronous spherical motors

Nonlinear optimal control for permanent magnet synchronous spherical motors

Design optimization to minimize wake of wide-body transport aircraft

A cutting-edge sustainable airplane can improve performance and enhance profitability are the most significant future concerns for the aviation industry. This research aims to analyse and assess aircraft performance of mid-size transport aircraft through retrofit designs. An optimal design was employed using a non-linear optimization approach under two cases fuselage alone (case 1) and a combination of fuselage-wing-empennage (case 2). These two retrofit concepts were evaluated and compared with the baseline A310–200 aircraft. To compute the objective function for various cases, non-linear solver was used from MATLAB optimization tool box. Additionally, the parametric studies of aerodynamics, structural and operational performance analysis are carried out by using Advanced Aircraft Analysis (AAA) 5.0 software. Sensitivity analyses are performed to assess the overall effectiveness of the optimal design. The key findings of this paper obtained the following parameters as Maximum take-off Weight, empty weight, fuel weight, parasite drag coefficient, rate of climb, take-off distance and landing distance are improved by 0.36%, 26.02%, 10.12%, 4.48%, 27.24%, 13.13% and 9.2% respectively. At the end, the paper provides a clear statement on the managerial perceptions and future insights for the upcoming challenges towards sustainable design.