Nonlinear Optimization Method Research Articles

Optimization of gas extraction of producing wells to increase the efficiency of condensate production

The article discusses ways to increase the efficiency of condensate production due to the optimal distribution of gas flows between producing wells. For a large number of wells, the solution of this problem becomes nontrivial and requires special methods of nonlinear optimization. The main aim of research is obtaining accurate solutions to the problem of optimizing condensate production using direct dependencies between gas and condensate production. The minimum set of reliable field information has been determined, which allows solving the problem of optimal distribution of gas production between wells at the maximum condensate flow rate. An optimization problem is formulated for this model. The conditions under which the initial problem is divided into a system of optimization subtasks for subgroups of wells are considered. By the method of pairwise optimization, analytical expressions were found for optimal ratios of gas flow rates in a group of wells. Based on the expressions obtained, an algorithm has been developed for the exact solution of the problem of short-term optimization of the well operation mode.

THE METHOD OF OPTIMIZING THE DISTRIBUTION OF RADIO SUPPRESSION MEANS AND DESTRUCTIVE SOFTWARE INFLUENCE ON COMPUTER NETWORKS

Context. Currently, generalized methodical approaches to the development of scenarios of complex radio suppression and electromagnetic influence of typical special telecommunication systems have been developed. However, during the development of possible cases for the complex application of radio suppression and destructive software influence,the problem of optimizing the resource of these means and its distribution according to the goals of radio suppression and objects of destructive computer influence arose, which has not yet been fully resolved.Especially in the literature known to the authors, there is no method for optimizing the resource distribution of radio and computer influence, used for the development and practical implementation of optimal scenarios of destructive influence on computer networks of enemy military groups in military operations.
 Therefore, it is necessary to formulate a problem and develop a method of optimizing the distribution of the resource of radio suppression and destructive software influence for the development of possible scenarios of the enemy’s violation of information exchange in a standart telecommunication network.
 Objective. The purpose of the research is to develop a method for optimizing the distribution of the resource of radio suppression and destructive software influence for the development of scenarios of information exchange violations by the enemy in the telecommunications network.
 Method.To achieve the purpose of the research, the methods of nonlinear optimization of heterogeneous resource distribution, mass service theory, and expert evaluation were comprehensively applied and developed in the field of modeling of information conflict.
 To determine the coefficients of protection of objects from radio-electronic and destructive computer influence, expert evaluation methods are used, in particular, the method of frequencies of preferences of the decision-maker using the Thurstone method. This method requires only one expert (a decision-maker), minimal communication time with him, minimal expert information (full ordering of weighting factors) and can be applied with a small number of evaluated weighting factors.
 To solve the problem of optimal distribution of a heterogeneous resource of means of destructive influence, to ensure the value of the multiplicative objective function of an arbitrary form is not less than the given one, the method of successive increments is applied.
 To determine the efficiency indicator of information exchange violation, the methods of mass service theory are applied, which allows to formalize special telecommunication systems as a set of mass service systems – subsystems of digital communication and computer networks.
 Results. The formulated problem and the entered indicators made it possible to solve the problem of determining the minimum resource of means of destructive influence and their optimal distribution according to the purposes of radio suppression on the objects of destructive program influence in order to achieve the required level of disruption of the efficiency of information exchange in special telecommunication systems.
 Conclusions.According to the results of the article, a method for optimizing the distribution of the resource of radio suppression and destructive software influence has been developed for the development of possible scenarios of information exchange violations by the enemy in a typical telecommunications network.The verification of the proposed method was carried out by comparing the theoretical results with the results of simulated modeling of scenarios of violation of the information exchange in the telecommunications network by the enemy.

Nonlinear optimal control for the multi-variable tumor-growth dynamics

The multivariable tumor-growth dynamic model has been widely used to describe the inhibition of tumor-cells proliferation under the simultaneous infusion of multiple chemotherapeutic drugs. In this article, a nonlinear optimal (H-infinity) control method is developed for the multi-variable tumor-growth model. First, differential flatness properties are proven for the associated state-space description. Next, the state-space description undergoes approximate linearization with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices. The linearization process takes place at each sampling instant around a time-varying operating point which is defined by the present value of the system’s state vector and by the last sampled value of the control inputs vector. For the approximately linearized model of the system a stabilizing H-infinity feedback controller is designed. To compute the controller’s gains an algebraic Riccati equation has to be repetitively solved at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. Finally, the performance of the nonlinear optimal control method is compared against a flatness-based control approach.

Nonlinear optimal and multi-loop flatness-based control of induction motor-driven desalination units

In this article, the control problem for the induction-motor driven reverse osmosis in desalination units is solved with the use of (i) a nonlinear optimal control method (ii) a flatness-based control approach which is implemented in successive loops. To apply method (i) that is nonlinear optimal control, the dynamic model of the induction-motor driven reverse-osmosis desalination units undergoes approximate linearization at each sampling instant with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices. The linearization point is defined by the present value of the system’s state vector and by the last sampled value of the control inputs vector. To compute the feedback gains of the optimal controller an algebraic Riccati equation is repetitively solved at each time-step of the control algorithm. The global stability properties of the nonlinear optimal control method are proven through Lyapunov analysis. To implement control method (ii), that is flatness-based control in successive loops, the state-space model of the induction-motor driven reverse-osmosis desalination unit is separated into three subsystems, which are connected in cascading loops. Each one of these subsystems can be viewed independently as a differentially flat system and control about it can be performed with inversion of its dynamics as in the case of input–output linearized flat systems. The state variables of the preceding (ith) subsystem become virtual control inputs for the subsequent (i+1th) subsystem. In turn, exogenous control inputs are applied to the first and third subsystem. The whole control method is implemented in three successive loops and its global stability properties are also proven through Lyapunov stability analysis. The proposed method achieves stabilization of the induction-motor-driven reverse osmosis desalination unit without the need of diffeomorphisms and complicated state-space model transformations.

Inversion of mine ventilation resistance coefficients enhanced by deep reinforcement learning

The ventilation resistance coefficients of a mine is vital to ventilation system safety management, diagnosis, and intelligentization. Airflow typically serves as the basis for inverting ventilation resistance coefficients. However, the issue of non-uniqueness in conventional nonlinear optimization methods affects the accuracy of inversion. Therefore, this study introduces a novel optimization approach based on deep reinforcement learning (DRL) to invert resistance coefficients. In this methodology, inversion is regarded as a Markov decision process, with the ventilation network solving model (VNSM) embedded within the DRL environment. We design an agent utilizing deep neural networks, which dynamically adjusts the resistance coefficient state variables by interacting with the VNSM to enhance the consistency between theoretical and measured airflow. The consistency corresponds to the agent’s reward. The proximal policy optimization is employed to optimize the agent’s policy. In field experiment, the MAE between the airflow calculated and the measured airflow is 0.354, with MSE of 0.287, RMSE of 0.536, and MRE of 0.013. Compared with the standard genetic algorithm, differential evolution algorithm, and evolution strategy algorithm, the DRL method shows lower MRE, MAE, RMSE, and MSE values by 23.5%, 15.3%, 14.1%, and 26.4%, respectively. Additionally, DRL method exhibits smaller sensitivity differences for different roadways than others algorithm.

A Comparison of Nonlinear Optimization Methods for Rosenbrock, Booth, and Matyas Functions

There is increasing interest in the application of nonlinear optimization techniques across a broad range of real-world problems that is linked to rapid advances in novel technologies and renewed interest in areas like sustainable development. While many algorithms for nonlinear optimization have been developed, they differ widely in their methods of convergence to the solution. Consequently, matching the function to be optimized with the right optimization algorithm is essential. To further explore this relationship, we studied two nonlinear optimization methods – the Nelder-Mead simplex method that only performs function evaluations and the quasi-Newton method which requires estimation of derivatives. These algorithms were used to find the global minima of the Rosenbrock, Booth, and Matyas functions from multiple starting points. The convergence paths for each starting point across both optimization methods for all 3 functions were visualized on contour plots. While convergence on the global minima was observed in all instances, our analysis indicated that the quasi-Newton method was consistently more efficient and needed fewer iterations than the Simplex method. This was especially pronounced for the Booth and Matyas functions where ~10-fold and 20-fold fewer iterations, respectively, were necessary for convergence. Our analysis reinforces the need to carefully match properties of the function being minimized with the performance characteristics of the optimization approach to obtain fast convergence on the global minimum.

Targeted Observations on Arctic Sea Ice Concentration for Improving Extended‐Range Prediction of Ural Blocking

AbstractThe predictability of certain extreme weather events can exceed the traditional 2 weeks by considering the boundary conditions. Targeted observations in sensitive areas (SA) on Arctic sea ice concentration (SIC) can improve the extended‐range (4 pentads) forecast skills of long‐lasting and strong Ural blocking (UB). The SA are determined based on the SIC optimally growing boundary errors, obtained by the conditional nonlinear optimal perturbation method. The SA are mainly located in the Barents Sea, Greenland Sea, and Okhotsk Sea. The results of observing system simulation experiments for 8 UB cases indicate that the targeted observations can remarkably improve the prediction skills of UB in the fourth pentad. Targeted observations have a positive effect on 75% of 160 experiment members, reduce 35% forecast errors of the fourth pentad mean blocking index, and perform even better when the original forecast errors are greater. Further diagnosis shows that targeted observations contribute to more accurate SIC boundary conditions in the Barents Sea, Greenland Sea, and Okhotsk Sea and reduce temperature errors in the lower and middle troposphere. It further results in well‐described westerly winds in the Ural region and its adjacent regions, corresponding to the more skillful predictions of blocking circulations. The above results supply a theoretical base for the design of Arctic SIC observations and more skillful extended‐range predictions for mid‐latitude extreme weather.

Time-dependent reliability-based design optimization of main shaft bearings in wind turbines involving mixed-integer variables

Main shaft bearings are essential transmission components in wind turbines. The failure of the main shaft bearings is inevitably accompanied by catastrophic consequences. In this regard, this paper presents a time-dependent reliability-based design optimization (TRBDO) approach for main shaft bearings involving mixed-integer variables. The maximization of fatigue life and the elastohydrodynamic film thickness under the load spectrum are selected as optimization objectives. The time-dependent reliability and geometric correlation are determined as nonlinear constraints. An efficient two-stage enrichment strategy is introduced to handle the time-dependent probabilistic constraint with mixed-integer design variables. A mixed-integer nonlinear optimization method is developed based on a meta-heuristic algorithm to solve the formulated TRBDO problem. Eventually, the effectiveness and robustness of the proposed approach are demonstrated by a real application in a 5 MW wind turbine.

Quadratic Programming for Continuous Control of Safety-Critical Multiagent Systems Under Uncertainty

This paper studies the control problem for safety-critical multi-agent systems based on quadratic programming (QP). Each controlled agent is modeled as a cascade connection of an integrator and an uncertain nonlinear actuation system. In particular, the integrator represents the position-velocity relation, and the actuation system describes the dynamic response of the actual velocity to the velocity reference signal. The notion of input-to-output stability (IOS) is employed to characterize the essential velocity-tracking capability of the actuation system. The standard QP algorithms for collision avoidance may be infeasible due to uncertain actuator dynamics. Even if feasible, the solutions may be non-Lipschitz because of possible violation of the full rank condition of the active constraints. Also, the interaction between the controlled integrator and the uncertain actuator dynamics may lead to significant robustness issues. Based on the current development of nonlinear control theory and numerical optimization methods, this paper first contributes a new feasible-set reshaping technique and a refined QP algorithm for feasibility, robustness, and local Lipschitz continuity. Then, we present a nonlinear small-gain analysis to handle the inherent interaction for guaranteed safety of the closed-loop multi-agent system. The proposed method is illustrated by numerical simulation and a physical experiment.

Adaptive Spectral Inversion for inverse medium problems

A nonlinear optimization method is proposed for the solution of inverse medium problems with spatially varying properties. To avoid the prohibitively large number of unknown control variables resulting from standard grid-based representations, the misfit is instead minimized in a small subspace spanned by the first few eigenfunctions of a judicious elliptic operator, which itself depends on the previous iteration. By repeatedly adapting both the dimension and the basis of the search space, regularization is inherently incorporated at each iteration without the need for extra Tikhonov penalization. Convergence is proved under an angle condition, which is included into the resulting Adaptive Spectral Inversion (ASI) algorithm. The ASI approach compares favorably to standard grid-based inversion using L 2-Tikhonov regularization when applied to an elliptic inverse problem. The improved accuracy resulting from the newly included angle condition is further demonstrated via numerical experiments from time-dependent inverse scattering problems.

A novel binocular vision-robot hand-eye calibration method using dual nonlinear optimization and sample screening

To reduce the effects of random errors in vision robotic systems, a double-layer LM (Levenberg- Marquardt) optimization (DLMO) method was designed to improve the calibration accuracy of the robot hand-eye matrix based on the principle of nonlinear optimization. Firstly, a hand-eye matrix equation was established, and the initial value of the hand-eye matrix was solved by using a linear least square method. Secondly, Euler angle transformation was performed on the rotation matrix part in the hand-eye matrix, to ensure the orthogonality of the rotation matrix. Then, an optimization model of the hand-eye matrix was constructed, and the initial value of the hand-eye matrix was optimized for the first time by using the traditional LM nonlinear optimization method. Finally, the optimization model of the hand-eye matrix was modified, and then the LM nonlinear optimization method with the function of sample point screening was used to optimize the hand-eye matrix for the second time. Using the proposed DLMO, the hand-eye calibration tests were carried out on two industrial robots equipped with binocular vision systems. The average position errors of the calibration results were 0.33 mm and 0.51 mm, respectively. The results showed that the accuracy of the proposed calibration method met the working requirements of the vision-robot in the industrial field.

Automated Design of Synthetic Gene Circuits in the Presence of Molecular Noise.

Microorganisms (mainly bacteria and yeast) are frequently used as hosts for genetic constructs in synthetic biology applications. Molecular noise might have a significant effect on the dynamics of gene regulation in microbial cells, mainly attributed to the low copy numbers of mRNA species involved. However, the inclusion of molecular noise in the automated design of biocircuits is not a common practice due to the computational burden linked to the chemical master equation describing the dynamics of stochastic gene regulatory circuits. Here, we address the automated design of synthetic gene circuits under the effect of molecular noise combining a mixed integer nonlinear global optimization method with a partial integro-differential equation model describing the evolution of stochastic gene regulatory systems that approximates very efficiently the chemical master equation. We demonstrate the performance of the proposed methodology through a number of examples of relevance in synthetic biology, including different bimodal stochastic gene switches, robust stochastic oscillators, and circuits capable of achieving biochemical adaptation under noise.

An inverse kinematics solution with trajectory scaling for redundant manipulators

Kinematic redundancy offers robots many useful capabilities, such as an ability to fulfill several tasks simultaneously. However, the inverse kinematics (IK) problem for redundant manipulators is not trivial. Often, pseudoinverse-based methods are used, allowing for the projection of the desired joint space velocity vector on the null space of the manipulator’s Jacobian. Unfortunately, it is not straightforward to include in the solution the joint position, velocity and acceleration bounds. On the other hand, the IK problem can be formulated as an optimization problem. A quadratic programming (QP) formulation is especially attractive for an online implementation, since it is computationally much lighter than nonlinear optimization methods. In a QP IK formulation, the joint constraints can be easily included. However, if the desired end effector trajectory becomes too demanding, then the joint space solution might not exist. To overcome this obstacle, we propose a QP IK formulation with trajectory scaling. The method is successfully tested on a model of KUKA LWR4+ 7-DOF manipulator; the joint constraints are satisfied and the motion is slowed down only when it is necessary.

SPSVO: a self-supervised surgical perception stereo visual odometer for endoscopy

AbstractAccurate tracking and reconstruction of surgical scenes is a critical enabling technology toward autonomous robotic surgery. In endoscopic examinations, computer vision has provided assistance in many aspects, such as aiding in diagnosis or scene reconstruction. Estimation of camera motion and scene reconstruction from intra-abdominal images are challenging due to irregular illumination and weak texture of endoscopic images. Current surgical 3D perception algorithms for camera and object pose estimation rely on geometric information (e.g., points, lines, and surfaces) obtained from optical images. Unfortunately, standard hand-crafted local features for pose estimation usually do not perform well in laparoscopic environments. In this paper, a novel self-supervised Surgical Perception Stereo Visual Odometer (SPSVO) framework is proposed to accurately estimate endoscopic pose and better assist surgeons in locating and diagnosing lesions. The proposed SPSVO system combines a self-learning feature extraction method and a self-supervised matching procedure to overcome the adverse effects of irregular illumination in endoscopic images. The framework of the proposed SPSVO includes image pre-processing, feature extraction, stereo matching, feature tracking, keyframe selection, and pose graph optimization. The SPSVO can simultaneously associate the appearance of extracted feature points and textural information for fast and accurate feature tracking. A nonlinear pose graph optimization method is adopted to facilitate the backend process. The effectiveness of the proposed SPSVO framework is demonstrated on a public endoscopic dataset, with the obtained root mean square error of trajectory tracking reaching 0.278 to 0.690 mm. The computation speed of the proposed SPSVO system can reach 71ms per frame.

Proton LET Optimization Via Iterative Convex Relaxation Method

If not optimized, the LET distribution can greatly impact normal tissue toxicity near tumor targets, because the LET often peaks at the distal edge of Bragg peak. LET optimization can account for biological effectiveness of protons during treatment planning, for minimizing biological proton dose and hot spots to normal tissues. However, the LET optimization is nonlinear and nonconvex to solve, which poses a great challenge in optimization. This work will develop an effective LET optimization method via iterative convex relaxation (ICR). In contrast to the generic nonlinear optimization method, such as Quasi-Newton (QN) method, that does not account for specific characteristics of LET optimization, ICR is tailored to LET modeling and optimization in order to effectively and efficiently solve the LET problem. Specifically, nonlinear dose-averaged LET term is iteratively linearized and becomes convex during ICR, while nonconvex dose-volume constraint and minimum-monitor-unit constraint are also handled by ICR, so that the solution for LET optimization is obtained by solving a sequence of convex and linearized convex subproblems. Since the high LET mostly occurs near the target, a 1cm normal-tissue expansion of clinical target volume (CTV) (excluding CTV), i.e., CTV1cm, is defined to as an auxiliary structure during treatment planning, where LET is minimized. ICR was validated in comparison with QN for abdomen, lung, and head-and-neck (HN) cases. ICR was effective for LET optimization, as ICR substantially reduced the LET and biological dose in CTV1cm the ring, with preserved dose conformality to CTV. Compared to QN, ICR had smaller LET, physical and biological dose in CTV1cm, and higher conformity index values; ICR was also computationally more efficient, which was about 3 times faster than QN. A lung case is presented in the table, where the quantities from top to bottom are computational time T (unit: second); total objective F, dose objective Fd and LET objective FL (unit: 10-3); conformity index for physical dose CId and biological dose CIb; mean LET L (unit: keV/μm), mean physical dose d and mean biological dose b (in ratio to prescription dose) for CTV1cm; mean LET L (unit: keV/μm), mean physical dose d and mean biological dose b (in ratio to prescription dose; unit: 10-1) for the heart. A LET-specific optimization method based on ICR has been developed for solving proton LET optimization, which has been shown to be more computationally efficient than generic nonlinear optimizer via QN, with better plan quality in terms of LET, biological and physical dose conformality.

Nonlinear Dynamic Model-Based Position Control Parameter Optimization Method of Planar Switched Reluctance Motors

Currently, there are few systematic position control parameter optimization methods for planar switched reluctance motors (PSRMs); how to effectively optimize the control parameters of PSRMs is one of the critical issues that needs to be urgently solved. Therefore, a nonlinear dynamic model-based position control parameter optimization method of PSRMs is proposed in this paper. First, to improve the accuracy of the motor dynamics model, a Hammerstein–Wiener model based on the BP neural network input–output nonlinear module is established by combining the linear model and nonlinear model structures so that the nonlinear and linear characteristics of the system are characterized simultaneously. Then, a position control parameter optimization system of PSRMs is developed using the established Hammerstein–Wiener model. In addition, with a self-designed simulated annealing adaptive particle swarm optimization algorithm (SAAPSO), the position control parameter optimization system is performed offline iteratively to obtain the optimal position control parameters. Simulations and experiments are carried out and the corresponding results show that the optimal position control parameters obtained by the proposed method can be directly applied in the actual control system of PSRMs and the control performance is improved effectively using the obtained optimal control parameters.

An efficient LightGBM-based differential evolution method for nonlinear inelastic truss optimization

A metaheuristic-based structural optimization method, whilst being popularly adopted due to its advantages in by-passing gradient function calculations, requires the use of time-consuming advanced analyses for constraint evaluation. To overcome this drawback, the present paper proposes a robust (machine learning-based) optimization method that combines the light gradient boosting machine (LightGBM) with the efficient p-best differential evolution (EpDE) method. In essence, the LightGBM classification model is constructed to assess the constraint (safety and integrity) satisfaction of structures. An efficient framework using a so-called safety parameter is proposed to prevent inaccurate predictions of the LightGBM model. The EpDE processes the optimization procedures on the constructed classification LightGBM model. This enables an enhanced machine learning-based optimization technique that not only maintains the sufficiently accurate optimal design of structures but also significantly reduces the required computing efforts, as compared to standard optimization schemes. Various examples of steel structure designs (i.e., two of which have been provided herein) have been successfully performed by the proposed approach. These illustrate the accuracy and robustness of the proposed method, where good comparisons with reference algorithms (including standard DE with “DE/rand/1” mutational strategy, Jaya, Rao-1 and CaDE) are evidenced. The statistical values collected present the accuracy and reliability of the proposed method in obtaining the minimum total weight designs with substantial (some 60%) reduction of computing efforts required to furnish optimal results.

Nonlinear optimal control for permanent magnet synchronous spherical motors

Nonlinear optimal control for permanent magnet synchronous spherical motors

Optimization of Rectangular and Box Sections in Oblique Bending and Eccentric Compression

The article presents a solution to the problem of finding the optimal ratio of the height of the cross-section to the width for a rectangular and box-shaped section in the case of oblique bending and eccentric compression. Optimization is performed according to the strength criterion, and for the case of oblique bending of a rectangular beam, a solution was also obtained from the condition of a minimum full deflection. For a rectangular section, the solution is made analytically, and for a box section, numerically using the MATLAB environment and the Optimization Toolbox package. As a numerical method of nonlinear optimization, the interior point method is used. To simplify the solution, the box section is assumed to be thin-walled, i.e. it is assumed that the wall thickness is significantly less than the height and width of the cross section. An estimate of the error of such an assumption is also performed. It has been established that in the case of oblique bending of a rectangular beam, when optimizing according to the strength criterion, the optimal ratio of the cross-sectional height to width is equal to the cotangent of the angle between the force plane and the vertical axis, and when optimizing according to the rigidity criterion, it is the square root of the cotangent of this angle. In the case of eccentric compression of a rectangular beam with eccentricities in two planes, the optimal ratio of the height of the cross section to the width is equal to the ratio of the eccentricity along the vertical and horizontal axes. For a box-shaped section, graphs of the change in optimal parameters depending on the angle between the force plane and the vertical axis in the case of oblique bending, as well as depending on the ratio of eccentricities along the axes in the case of eccentric compression, are plotted.

High Precision Mass Balancing Method for the Fourth Harmonic of Mass Defect of Fused Quartz Hemispherical Resonator Based on Ion Beam Etching Process

In this paper, a novel ultra-high precision mass balancing method for fused quartz hemispherical resonator based on the ion beam etching process is proposed from the perspective of vibration mechanics. Firstly, the motion equations of resonator with mass defect are established to reveal the quantitative relationship between the amplitude of defective mass and frequency split, and the geometrical relationship between the distribution of defective mass and eigenfrequency axis, which is the equivalent morphology of mass defect. Secondly, according to the motion equations, the radial vibration model of resonator lip edge is deduced, then a new identification model for the vibration parameters composed of the frequency split, mechanical time constant, and azimuth of eigenfrequency axis based on the vibration envelope and spectral analysis is established. The vibration parameters are identified by nonlinear optimization method. After that, the mass removal function and etching efficiency function of ion beam acting on the resonator are calibrated by experimental data, then the etching trajectory is planned and the etching time is calculated. Finally, the experimental result of mass balancing indicates that the frequency split is reduced from 0.2354Hz to 0.0006Hz, and the quality factor is greater than 2.2×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7</sup> , which can significantly improve the vibration performance of resonator.