Sequential Quadratic Programing Research Articles

Heuristic computing performances based Gudermannian neural network to solve the eye surgery corneal model

The current work is related to present the solutions of the corneal shape-based eye surgery model (CSESM) by applying the novel procedures of Gudermannian neural network (GNN) along with the hybrid optimization of the global and local approaches of heuristic genetic algorithm (GA) and sequential quadratic programing (SQP), i.e., GNN-GASQP. An error function is constructed using the terminologies of the differential model along with the corresponding boundary conditions of the CSESM and then the optimization of the parameter is approved by the global operator GA at the start and then local refinements of SQP is implemented. Six different cases of the CSESM have been numerically treated using the GNN-GASQP and the scheme’s correctness is performed through the numerical Runge-Kutta (RK) results. The analysis based small and larger neurons is also implemented to authenticate the stability of GNN-GASQP. Moreover, the analysis through statistics using different measures of root mean square error, Theil’s inequality coefficient and variance account for is presented to check the consistency of GNN-GASQP for solving the CSESM.

Vehicle pitch dynamics control using in-wheel motors

Implementation of in-wheel motors brings numerous advantages: decreased overall vehicle weight and manufacture cost, available accurate torque control for better road handling and powertrain high energy efficiency. Even so, when the motor is placed inside the wheel, the unsprung mass of the vehicle increases, leading to a less comfortable ride. This paper puts forward and studies a control system that takes advantage of the vertical component of the driving force provided by an in-wheel motor to enhance ride comfort and handling dynamics. The proportional integral (PI) controller was proposed to minimize the pitch acceleration response of the vehicle. Controller’s gains were optimized using the gradient descent method with sequential quadratic programing algorithm. A co-simulation approach and a dynamic model of the vehicle were presented. Data regarding the vehicle’s measurements was taken from a real car with in-wheel motors. The dynamic model of the car was validated based on the results derived during the road test experiment. Assessing the controller’s effectiveness, a co-simulation approach between the dynamic model and the control system was established. An acceleration test in a straight line showed a 25% increase in ride comfort as measured by the RMS pitch angular vibrations of the sprung mass. The control is attained with no increase in the tire load and the vehicle’s longitudinal dynamics.

Selection of design parameters of working coil for Al/Cu tubular Magnetic Pulse Welding

MPW produces a high Lorentz force for welding through the interaction of magnetic fields between the working coil and outer workpiece. Therefore, the design of the working coil is crucial in the MPW process. In particular, it is important to understand and estimate the distribution of Lorentz force on the outer tube and the stress on the working coil. These factors greatly impact the efficiency of energy delivery and the durability of the process. The purpose of this research was to analyze the effect of coil design parameters on the Lorentz force and stress. The ultimate objective was to optimize these design parameters specifically for welding tubular workpieces; for this, an electromagnetic-mechanical FE-model was developed. The design parameters considered in this study included the angle, radius, and protruding length. The Lorentz force and stress were calculated based on these parameters. Notably, the response surface method (RSM) and sequential quadratic programing (SQP) were utilized to develop a prediction model and optimize the design parameters, respectively. The findings revealed that the protruding length and angle are significant design parameters. Consequently, a working coil was manufactured using the optimized design parameters, leading to a successful Al/Cu joint. These results emphasize the indispensability of optimizing design parameters to achieve high-quality joints.

Parametric scatterer extraction method for space‐target inverse synthetic aperture radar image CLEAN

AbstractOwing to the time variance of the inverse synthetic aperture radar (ISAR) imaging plane of space targets, scatterers with large heights relative to the imaging plane migrate through several Doppler cells. This defocussing in the azimuth direction of each scatterer cannot be compensated via the traditional migration through the resolution cell (MTRC) compensation method because the height of each scatterer is quite different and independently distributed in the ISAR image. In this study, a parametric azimuth‐defocussing model‐based CLEAN method is proposed for the space‐target ISAR image. First, high‐order defocus parameters and their influences on the image of space targets were analysed at different arc segments. Subsequently, a mathematical azimuth‐defocussing expression of the ISAR image scatterers was derived after MTRC and azimuth high‐order phase compensation, and an approximate defocus expression based on the Fresnel integral was provided for computational efficiency. This model can estimate the complex amplitude, coordinates and defocus parameters of each scatterer in the image domain by applying a sequential quadratic programing algorithm. Finally, the validity and stability of the proposed algorithm for the isolated and coupled scatterer extraction were verified at different signal‐to‐noise ratios, and different defocus parameters were verified through simulations.

Parallelized optimization for substructured finite element structural acoustic problems

This work explores the use of parallelized optimization techniques for structural acoustics problems. In particular, the underlying problems studied here utilize finite element substructuring in order to solve the objective function, though the substructuring aspect is not the primary focus of this work. Instead, several different optimization strategies were employed on a selection of problems to better understand the tradeoffs between the different algorithms. Throughout this effort, the Python library PyGMO is used due to its capabilities to wrap around many different optimization algorithms and distribute optimization tasks over multiple CPUs. The candidate algorithms studied in this work include both heuristic global optimizers and gradient based local optimizers such as the following: Extended Ant Colony (GACO), Conjugate Gradient (CG), Sequential Quadratic Programing (SLSQP), and Method of Moving Asymptotes (MMA). Each method is evaluated individually as well as in combination with some or all of the others to evaluate if a mixed algorithm approach is advantageous. A range of computational resources are employed to understand the scalability and other aspects of the parallelized calculations.

Multi-objective macrogeometry optimization of gears: Comparison between sequential quadratic programing and genetic algorithm

Deciding a gear pair’s macrogeometry parameters requires consideration of the factors such as cost of production, gear strength, and noise contributing parameters. A practical engineering problem is encountered when best possible gear geometry is needed for a fixed center distance to achieve the conflicting objectives. Further, constraints of practical utility on input parameters need to be taken into consideration for deciding the design space. This work represents comprehensive compilation of formulations of these often-conflicting objectives and constraints as non-linear functions and selection of an appropriate optimization technique to achieve a feasible design through a case study of a helical gear pair in high load carrying capacity mesh. For comparison of the quality of results and computational efficiency between gradient based and gradient free algorithms, Sequential Quadratic Programming and Genetic algorithm were used. The differences in the formulations of the objective functions for two algorithms were analyzed and addressed. Quadratic mutation rates and random crossovers were used to prevent premature convergence of Genetic Algorithm. Significant possible improvement in the base design was observed with both the algorithms.

Online cooperative airspace conflict resolution of unmanned aerial vehicles by space mapping based iterative search method

This paper presents an investigation into the locally centralized conflict resolution problem of unmanned aerial vehicles (UAVs), in which the headings are adjustable variables. Firstly, the geometric characteristics of the conflict resolution problem in two-dimensional space are studied, and the problem is reduced into a nonlinear programing model. Secondly, the nonlinear safe separation constraint is transferred into linear style in the sine value space using the space mapping method. The feasible region of two conflict-related UAVs is transformed into a half-space in the sine value space. The minimum adjustment vector and the maximum adjustable vector are obtained in this space. Thirdly, to search for the local optimal conflict-free solution, a two-layered optimization method is given. In the first layer, feasible conflict-free solutions are obtained by iterative search in virtue of the minimum adjustment vector and the maximum adjustable vector. In the second layer, the local optimal solution is generated using the sequential quadratic programing (SQP) method. The effectiveness of the proposed method is verified by numerical simulations. Compared with the existing geometric guidance theory based methods, the proposed method could effectively generate conflict-free solutions that lead to fewer detours, through which UAVs could coordinate online in highly crowded airspace.

Joint power and blocklength optimization for RIS‐aided multiple‐access downlink ultra‐reliable low‐latency communication

Ultra-reliable low-latency communication (URLLC) has gained significant interest since it deals with short packet transmission adopted to reduce latency; however, this implies that the conventional Shannon capacity formula is not applicable, and the achievable data rate becomes a complex function of the decoding error probability and blocklength. This paper studies URLLC transmission using a time-division multiple access scheme with an arbitrary number of actuators utilising a reconfigurable intelligent surface. The authors optimisze the weighted sum rate of this system subject to reliability, total energy, and latency constraints. For the blocklength allocation in a scenario where each actuator is allocated equal power, a closed-form analytical solution is provided. Also, for the case of joint optimization of the blocklength and power of each actuator, an analytical solution is provided for the case of two actuators, while an iterative sequential quadratic programing method is adopted for the case of an arbitrary number of actuators. The proposed methodology provides a low-complexity, fast solution, which is more efficient than using exhaustive search techniques. The results show that in some cases, optimization of the blocklength provides a near-optimal solution at low complexity, while jointly optimising the blocklength and the power per actuator has an improved performance at the cost of additional complexity.

Purification of methyl isobutyl ketone via dividing wall column with an internal boiling point of a heterogeneous azeotrope

Methyl isobutyl ketone (MIBK) is an important chemical product used in many fields and is mostly made by the acetone one-step method. It is difficult to extract high-purity MIBK from the reactants where complex azeotropes form, thus leading to traditional MIBK separation process at high energy cost and investments. In this study, a new separation process based on dividing wall column, HA-DWC-U, was developed considering the heterogeneous azeotrope with an internal boiling point. First, thermodynamic research was performed to assure the accuracy of the physical properties. The NRTL and UNIQUAC models were compared, of which some model parameters were regressed from experimental data, and two binary parameter data sets were set for the VLE and LLE calculations. Then, steady-state simulation and optimization of the traditional process and HA-DWC-U were performed, in which continuous variables were optimized in the inner loop using the sequential quadratic programing (SQP) method, while discrete variables were optimized in the outer loop using sensitivity analysis method. Remarkable, the results show that HA-DWC-U has obvious advantages over the traditional separation process, including 18.47% savings in total utility cost and 17.86% savings in total annual cost.

Implicit shock tracking for unsteady flows by the method of lines

A recently developed high-order implicit shock tracking (HOIST) framework for resolving discontinuous solutions of inviscid, steady conservation laws [43,45] is extended to the unsteady case. Central to the framework is an optimization problem which simultaneously computes a discontinuity-aligned mesh and the corresponding high-order approximation to the flow, which provides nonlinear stabilization and a high-order approximation to the solution. This work extends the implicit shock tracking framework to the case of unsteady conservation laws using a method of lines discretization via a diagonally implicit Runge-Kutta method by “solving a steady problem at each timestep”. We formulate and solve an optimization problem that produces a feature-aligned mesh and solution at each Runge-Kutta stage of each timestep, and advance this solution in time by standard Runge-Kutta update formulas. A Rankine-Hugoniot based prediction of the shock location together with a high-order, untangling mesh smoothing procedure provides a high-quality initial guess for the optimization problem at each time, which results in rapid convergence of the sequential quadratic programing (SQP) optimization solver. This method is shown to deliver highly accurate solutions on coarse, high-order discretizations without nonlinear stabilization and recover the design accuracy of the Runge-Kutta scheme. We demonstrate this framework on a series of inviscid, unsteady conservation laws in both one- and two- dimensions. We also verify that our method is able to recover the design order of accuracy of our time integrator in the presence of a strong discontinuity.

Optimization of Airfoil Blend Limits With As-Manufactured Geometry Finite Element Models

Abstract Conventional airfoil blend repair limits are established using nominal, design intent geometry. This convention does not explicitly consider the inherent blade-to-blade structural response variation associated with geometric manufacturing deviations. In this work, we explore whether accounting for these variations leads to significant differences in blend depths and develop a novel approach to effectively predict blade-specific blend allowable. These blade-specific values maximize the part repairability according to their proximity to defined structural integrity constraints. The methodology is demonstrated on the as-manufactured geometry of an aerodynamic research rig compressor rotor. Geometric point cloud data of this rotor is used to construct as-built finite element models (FEMs) of each airfoil. The effect of two large blends on these airfoils demonstrates the opportunity of blade-specific blend limits. A new approach to determine each airfoil's blend repair capacity is developed that uses sequential least-squares quadratic programing and a parametric blended blade FEM that accounts for manufacturing geometry variations and variable blend geometry. A mesh morphing algorithm modifies a nominal geometry model to match the as-built airfoil surface and blend geometry. The numerical optimization maximizes blend depth values within the frequency, mode shape, and high cycle fatigue constraint boundaries. It is found that there are large variations in blend depth allowable between blades and competing structural integrity criteria are responsible for their limits. It is also found that, despite complex modal behavior caused by eigenvalue veering, the proposed optimization approach converges. The developed methodologies may be used in the future to extend blend limits, enable continued operations, and reduce sustainment costs.

Multiobjective Macrogeometry Optimization of Gears: Comparison between Sequential Quadratic Programing and Genetic Algorithm

Multiobjective Macrogeometry Optimization of Gears: Comparison between Sequential Quadratic Programing and Genetic Algorithm

Evolutionary heuristic with Gudermannian neural networks for the nonlinear singular models of third kind

The presented research work articulates a new design of heuristic computing platform with artificial intelligence algorithm by exploitation of modeling with feed-forward Gudermannian neural networks (FFGNN) trained with global search viability of genetic algorithms (GA) hybrid with speedy local convergence ability of sequential quadratic programing (SQP) approach, i.e., FFGNN-GASQP for solving the singular nonlinear third order Emden-Fowler (SNEF) models. The proposed FFGNN-GASQP intelligent computing solver Gudermannian kernel unified in the hidden layer structure of FFGNN systems of differential operators based on the SNEF that are arbitrary connected to represent the error-based merit function. The optimization objective function is performed with hybrid heuristics of GASQP. Three problems of the third order SNEF are used to evaluate the correctness, robustness and effectiveness of the designed FFGNN-GASQP scheme. Statistical assessments of the performance of FFGNN-GASQP are used to validate the consistent accuracy, convergence and stability.

Reconstruction of Radiative Properties Fields in Participating Media by Using the Sequential Quadratic Programing Combined With Regularization Technique

The refractive index and absorption coefficient fields in participating media are reconstructed simultaneously in this work. In the direct model, the coupled radiation–conduction heat transfer in participating media exposed to a pulse laser irradiation is solved by finite volume method (FVM). In the inverse model, the sequential quadratic programming (SQP) algorithm combined with the generalized Gaussian Markov random field (GGMRF) model is employed to solve the reconstruction problem. It is found that the refractive index and absorption coefficient fields cannot be reconstructed simultaneously. A secondary reconstruction technique based on different regularization parameters is proposed to reconstruct the refractive index and absorption coefficient fields simultaneously. All the retrieval results indicate that the proposed secondary reconstruction technique performs accurately and effectively.

Closed-form solutions for the optimal design of inerter-based dynamic vibration absorbers

This paper is concerned with the development of novel closed-form solutions for the optimal design of inerter-based dynamic vibration absorbers by extending the Den Hartog's technique. Furthermore, in order to validate the closed solutions, an optimization problem for minimizing the standard deviation of difference among vibration amplitudes under an excitation frequencies range is formulated. Additionally, the numerical simulations showed that the extended fixed-points technique produces similar results than the H∞ optimization technique. The mechanical impedances studied in this research showed the best performance by minimizing the vibration amplitudes and maximizing the effective bandwidth of the classic Dynamic Vibration Absorber. The results showed that, by extending the fixed-points technique, a simplest alternative for the optimal design of IDVAs regardless of numerical methods, such as the sequential quadratic programing (SQP) or non-linear optimization techniques, was obtained.

Efficient hybrid algorithms to solve mixed discrete-continuous optimization problems

PurposeIn real-world cases, it is common to encounter mixed discrete-continuous problems where some or all of the variables may take only discrete values. To solve these non-linear optimization problems, the use of finite element methods is very time-consuming. The purpose of this study is to investigate the efficiency of the proposed hybrid algorithms for the mixed discrete-continuous optimization and compare it with the performance of genetic algorithms (GAs).Design/methodology/approachIn this paper, the enhanced multipoint approximation method (MAM) is used to reduce the original nonlinear optimization problem to a sequence of approximations. Then, the sequential quadratic programing technique is applied to find the continuous solution. Following that, the implementation of discrete capability into the MAM is developed to solve the mixed discrete-continuous optimization problems.FindingsThe efficiency and rate of convergence of the developed hybrid algorithms outperforming GA are examined by six detailed case studies in the ten-bar planar truss problem, and the superiority of the Hooke–Jeeves assisted MAM algorithm over the other two hybrid algorithms and GAs is concluded.Originality/valueThe authors propose three efficient hybrid algorithms, the rounding-off, the coordinate search and the Hooke–Jeeves search-assisted MAMs, to solve nonlinear mixed discrete-continuous optimization problems. Implementations include the development of new procedures for sampling discrete points, the modification of the trust region adaptation strategy and strategies for solving mix optimization problems. To improve the efficiency and effectiveness of metamodel construction, regressors f defined in this paper can have the form in common with the empirical formulation of the problems in many engineering subjects.

The Reduced Space Shooting Method for Calculating the Peak Periodic Solutions of Nonlinear Systems

A hybrid approach which combines the reduced sequential quadratic programing (SQP) method with the shooting method is proposed to search the worst resonance response of nonlinear systems. The shooting method is first employed to construct the nonlinear equality constraints for the constrained optimization problem. Then, the complex optimization problem is simplified and solved numerically by the reduced SQP method. By virtue of the coordinate basis decomposition scheme which exploits the gradients of nonlinear equality constraints, the nonlinear equality constraints are eliminated, resulting in a simple optimization problem subject to bound constraints. Moreover, the second-order correction (SOC) technique is adopted to overcome Maratos effect. The novelty of the approach described lies in the capability to efficiently handle nonlinear equality constraints. The effectiveness of the proposed algorithm is demonstrated by two benchmark examples seen in the literature.

An efficient aerodynamic shape optimization of blended wing body UAV using multi-fidelity models

This paper presents a novel optimization technique for an efficient multi-fidelity model building approach to reduce computational costs for handling aerodynamic shape optimization based on high-fidelity simulation models. The wing aerodynamic shape optimization problem is solved by dividing optimization into three steps—modeling 3D (high-fidelity) and 2D (low-fidelity) models, building global meta-models from prominent instead of all variables, and determining robust optimizing shape associated with tuning local meta-models. The adaptive robust design optimization aims to modify the shape optimization process. The sufficient infilling strategy—known as adaptive uniform infilling strategy—determines search space dimensions based on the last optimization results or initial point. Following this, 3D model simulations are used to tune local meta-models. Finally, the global optimization gradient-based method—Adaptive Filter Sequential Quadratic Programing (AFSQP) is utilized to search the neighborhood for a probable optimum point. The effectiveness of the proposed method is investigated by applying it, along with conventional optimization approach-based meta-models, to a Blended Wing Body (BWB) Unmanned Aerial Vehicle (UAV). The drag coefficient is defined as the objective function, which is subjected to minimum lift coefficient bounds and stability constraints. The simulation results indicate improvement in meta-model accuracy and reduction in computational time of the method introduced in this paper.

Application of constraint infeasibility detection methods in engineering design problems

PurposeThe purpose of this paper is to present numerical experimentation of three constraint detection methods to explore their main features and drawbacks in infeasibility detection during the design process.Design/methodology/approachThree detection methods (deletion filter, additive method and elasticity method) are used to find the minimum intractable subsystem of constraints in conflict. These methods are tested with four enhanced NLP solvers (sequential quadratic program, multi-start sequential quadratic programing, global optimization solver and genetic algorithm method).FindingsThe additive filtering method with both the multistart sequential quadratic programming and the genetic algorithm solvers is the most efficient method in terms of computation time and accuracy of detecting infeasibility. Meanwhile, the elasticity method has the worst performance.Research limitations/implicationsThe research has been carried out for only inequality constraints and continuous design variables. This research work could be extended to develop computer-aided graphical user interface with the capability of including equality constraints and discrete variables.Practical implicationsThese proposed methods have great potential for finding and guiding the designer to detect the infeasibility for ill-posed complex design problems.Originality/valueThe application of the proposed infeasibility detection methods with their four enhanced solvers on several mechanical design problems reduces the number of constraints to be checked from full set to a much smaller subset.

An Efficient Non-Gaussian Sampling Method for High Sigma SRAM Yield Analysis

Yield 1 analysis of SRAM is a challenging issue, because the failure rates of SRAM cells are extremely small. In this article, an efficient non-Gaussian sampling method of cross entropy optimization is proposed for estimating the high sigma SRAM yield. Instead of sampling with the Gaussian distribution in existing methods, a non-Gaussian distribution, i.e., a joint one-dimensional generalized Pareto distribution and ( n -1)-dimensional Gaussian distribution, is taken as the function family of practical distribution, which is proved to be more suitable to fit the ideal distribution in the view of extreme failure event. To minimize the cross entropy between practical and ideal distributions, a sequential quadratic programing solver with multiple starting points strategy is applied for calculating the optimal parameters of practical distributions. Experimental results show that the proposed non-Gaussian sampling is a 2.2--4.1× speedup over the Gaussian sampling, on the whole, it is about a 1.6--2.3× speedup over state-of-the-art methods with low- and high-dimensional cases without loss of accuracy