Direct Optimization Method Research Articles

Adaptive Concurrent Topology Optimization of Coated Structures with Nonperiodic Infill for Additive Manufacturing

The present research develops a direct multiscale topology optimization method for additive manufacturing (AM) of coated structures with nonperiodic infill by employing an adaptive mapping technique of adaptive geometric components (AGCs). The AGCs consist of a framework of macro-sandwich bars that represent the macrostructure with the solid coating and a network of micro-solid bars that represent the nonperiodic infill at the microstructural scale. The macrostructure including the coating skin and the internal architecture of the microstructures of cellular structures is simultaneously optimized by straightforwardly searching optimal geometries of the AGCs. Compared with most existing methods, the proposed method does not require material homogenization technique at the microscale; the continuity of microstructures and structural porosities are ensured without additional constraints; Finite element analysis (FEA) and geometric parameter updates are required only once for each optimization iteration. AGCs allow us to model coated structures with porosity infill on a coarse finite element mesh. The adaptive mapping technique may reduce mapping time by up to 50%. Besides, it is easy to control the length scales of the coating and infill as desired to make it possible with AM. This investigation also explores the ability to realize concurrent designs of coated structures with nonperiodic infill patterns using 3D printing techniques.

Optimum Design of Robust Adaptive Controller with Actuator Constraints

In this paper, a direct optimal adaptive nonlinear tracking control method for a class of uncertain Multi-Input Multi-Output (MIMO) nonlinear systems with actuator amplitude constraints in presence of unknown disturbance is developed. In order to handle parametric model uncertainties and external disturbance, an adaptive controller is presented. Particle Swarm Optimization (PSO) algorithm is employed to prevent constraints violation through determining the optimal adaptive controller parameters. The performance of this control approach is studied using a new index function in time-domain, and the stability analysis is conducted by Lyapunov theory. In addition, indicative robot examples are provided to illustrate how investigated method effectively stabilizes system and confines tracking error to prescribed bounds without control input saturation, particularly with large parametric uncertainties.

Efficient neural-network based variational Monte Carlo scheme for direct optimization of excited energy states in frustrated quantum systems

We examine applicability of the valence bond basis correlator product state ansatz, equivalent to the restricted Boltzmann machine quantum artificial neural network ansatz, and variational Monte Carlo method for direct optimization of excited energy states to study properties of strongly correlated and frustrated quantum systems. The energy eigenstates are found by stochastic minimization of the variational function for the energy eigenstates which allows direct optimization of particular energy state without knowledge of the lower energy states. This approach combined with numerous tensor network or artificial neural network ansatz wavefunctions then allows further insight into quantum phases and phase transitions in various strongly correlated models by considering properties of these systems beyond the ground state properties. Also, the method is in general applicable to any dimension and has no sign instability. An example that we consider is the square lattice J1-J2 antiferromagnetic Heisenberg model. The model is one of the most studied models in frustrated quantum magnetism since it is closely related to the disappearance of the antiferromagnetic order in the high-Tc superconducting materials and there is still no agreement about the properties of the system in the highly frustrated regime near J2/J1 = 0.5. For J1-J2 model we write the variational ansatz in terms of the two site correlators and in the valence bond basis and calculate lowest energy eigenstates in the highly frustrated regime near J2/J1 = 0.5 where the system has a paramagnetic phase. We find that our results are in good agreement with previously obtained results which confirms applicability of the method to study frustrated spin systems.

Convergence of the direct limit analysis design method for discrete topology optimization

The present paper addresses the robustness and convergence behavior of the direct limit analysis (LA) based methodology developed for the topology design of continuum structures subject to prescribed statically and plastically admissible loads. The design methodology, based on a direct method formulation of the static LA problem, has recently been proposed for continuous topology optimization and its merits were highlighted. One of its remarkable features is the outstanding similarity of the topology design mathematical problem with its underlying direct static form of the LA problem. Subsequently, it has been extended to solve two dimensional discrete, i.e. black-and-white, topology design problems by modifying the objective function into a square root form in a way to penalize the intermediate densities and solving a sequence of conic quadratic programming problems of identical scale and algebraic structure as the continuous design problem, leaving a number of issues to be investigated, pertaining to convergence. In the present work different families of penalization function forms are proposed and assessed as alternatives to the original square root function. The performance is evaluated in terms of robustness, accuracy in the sense of closeness of the final design to a 0–1 topology and efficiency or number of approximate problems required for convergence. Convergence of the discrete topology design is shown to be improved using higher order power functions as well as trigonometric and exponential type penalty functions. The performance of the design method in solving example problems using the various penalization schemes is compared and the factors that affect it are analyzed.

Hybrid optimization of low-thrust many-revolution trajectories with coasting arcs and longitude targeting for propellant minimization

Despite the ongoing advancements in low-thrust propulsion technology and the rise of all-electric satellite platforms, low-thrust spacecraft trajectory optimization remains a complex field of research. Shape-based approximations are predominant in interplanetary applications, but they are generally unsuitable for many-revolution trajectories, common in terrestrial applications. Indirect optimization methods allow for global optimization of many-revolution trajectories, but their mathematical complexity generally requires significant simplifications of the dynamical model, and they must be re-derived for any modification to the system dynamics or constraints. Conversely, direct optimization methods exhibit larger convergence radii and are flexible for application in different problems yet suffer from impractical computational times due to large design vectors.This paper presents a methodology for the optimization of low-thrust many-revolution trajectories, employing a hybrid combination of indirect and direct optimization methods. Similar hybrid approaches have been shown to be highly reliable for minimum-time trajectories. This methodology preserves similar performance while additionally enabling minimum-propellant optimization, through a mechanism that allows for coasting (non-thrusting) arcs, as well as targeting of the final geodetic-longitude. To reduce the propagation load of the methodology, we combine an orbital averaging scheme with a differential evolution algorithm, leading to a global optimization process with a practical computational effort. The analytical nature of the methodology reduces the number of optimization variables and its computational counterpart provides unmatchable flexibility for a configurable force and perturbation model as well as operational constraints fulfilment.The approach is applied to an unperturbed and a J2-perturbed GTO-GEO transfer, revealing a 0.03% and a 0.4% error, for time- and propellant-minimization respectively, relative to the reference optimal trajectories. This proves that the method can match the performance of former hybrid approaches while additionally allowing for engine on/off switching. Moreover, the inclusion of the J2 perturbation shows that, in contrast to indirect methods, it can accommodate modifications to the system dynamics without the need to re-derive the optimal control laws. Furthermore, a superior convergence radius of the optimization problem is demonstrated for the hybrid method, with respect to a reference indirect method, through the simultaneous optimization for minimum-propellant expenditure and final geodetic-longitude targeting. This research constitutes a significant advancement for space mission design and satellite operations, because it simultaneously harnesses the advantages of indirect and direct methods with broader flexibility than the popular indirect approaches and enhanced functionality than the former hybrid methods published in literature.

Battery package design optimization for small electric aircraft

The increasing gross weight of electric Unmanned Aerial Vehicle (UAV) poses a challenge in practical applications. The range and endurance of the electric UAV are limited by the fixed mass of the battery package. In this work, a design optimization method for the battery package topology of small electric UAV is proposed to enhance the performance. To improve the accuracy of the method, the dynamic battery model and simplified electric component models are presented. These models are utilized by the trajectory optimization method, which takes the dynamic characteristic into consideration to calculate the aircraft performance. The direct optimal control method is used for solving the trajectory optimization problem, and this method is tested on a small blended-wing-body electric aircraft. The test result shows that the range and energy-consumption are mainly influenced by the parallel topology of the battery package, while the flight time in climb phase is more sensitive to the series topology. It is deduced that the range- and energy-optimal design points can be considered concurrently in design optimization. The work proves the feasibility of integrating the trajectory optimization and battery package design.

Airborne electromagnetic data denoising based on dictionary learning

Time-domain airborne electromagnetic (AEM) data are frequently subject to interference from various types of noise, which can reduce the data quality and affect data inversion and interpretation. Traditional denoising methods primarily deal with data directly, without analyzing the data in detail; thus, the results are not always satisfactory. In this paper, we propose a method based on dictionary learning for EM data denoising. This method uses dictionary learning to perform feature analysis and to extract and reconstruct the true signal. In the process of dictionary learning, the random noise is filtered out as residuals. To verily the effectiveness of this dictionary learning approach for denoising, we use a fixed overcomplete discrete cosine transform (ODCT) dictionary algorithm, the method-of-optimal-directions (MOD) dictionary learning algorithm, and the K-singular value decomposition (K-SVD) dictionary learning algorithm to denoise decay curves at single points and to denoise profile data for different time channels in time-domain AEM. The results show obvious differences among the three dictionaries for denoising AEM data, with the K-SVD dictionary achieving the best performance.

Gradient-Based Particle Filter Algorithm for an ARX Model With Nonlinear Communication Output

A stochastic gradient (SG)-based particle filter (SG-PF) algorithm is developed for an ARX model with nonlinear communication output in this paper. This ARX model consists of two submodels, one is a linear ARX model and the other is a nonlinear output model. The process outputs (outputs of the linear submodel) transmitted over a communication channel are unmeasurable, while the communication outputs (outputs of the nonlinear submodel) are available, and both of the two-type outputs are contaminated by white noises. Based on the rich input data and the available communication output data, a SG-PF algorithm is proposed to estimate the unknown process outputs and parameters of the ARX model. Furthermore, a direct weight optimization method and the Epanechnikov kernel method are extended to modify the particle filter when the measurement noise is a Gaussian noise with unknown variance and the measurement noise distribution is unknown. The simulation results demonstrate that the SG-PF algorithm is effective.

A trajectory optimization method with frictional contacts for on-orbit capture

Using space robots to perform capture missions are challenging problems due to potential contacts. Most state-of-the-art techniques sidestep contacts by separating a capture mission into pre- and post-capture phases, and assuming the end-effector fixes to the target instantaneously. In this paper, frictional contacts have been taken into consideration, and a corresponding trajectory optimization method is developed. The frictional contact is formulated as two sets of complementarity constraints for the compression phase and the decompression phase. The direct method for trajectory optimization with complementarity constraints is established. The combination mechanism based on the sequential quadratic programming is proposed to solve resultant highly complex optimization problems, which can provide local optimal trajectories for space robots. The method is verified via numerical simulations of a planar dual-arm space robot capturing a spinning target, and results illustrate its great performance and potential usability on other scenarios.

Dynamic Optimization of a Fed-Batch Nosiheptide Reactor

Nosiheptide is a sulfur-containing peptide antibiotic, showing exceptional activity against critical pathogens such as methicillin-resistant Staphylococcus aureus (MRSA) and vancomycin-resistant Enterococci (VRE) with livestock applications that can be synthesized via fed-batch fermentation. A simplified mechanistic fed-batch fermentation model for nosiheptide production considers temperature- and pH-dependence of biomass growth, substrate consumption, nosiheptide production and oxygen mass transfer into the broth. Herein, we perform dynamic simulation over a broad range of possible feeding policies to understand and visualize the region of attainable reactor performances. We then formulate a dynamic optimization problem for maximization of nosiheptide production for different constraints of batch duration and operability limits. A direct method for dynamic optimization (simultaneous strategy) is performed in each case to compute the optimal control trajectories. Orthogonal polynomials on finite elements are used to approximate the control and state trajectories allowing the continuous problem to be converted to a nonlinear program (NLP). The resultant large-scale NLP is solved using IPOPT. Optimal operation requires feedrate to be manipulated in such a way that the inhibitory mechanism of the substrate can be avoided, with significant nosiheptide yield improvement realized.

Q-Law Aided Direct Trajectory Optimization of Many-Revolution Low-Thrust Transfers

Low-thrust spacecraft trajectory optimization for the many-revolution orbital transfer problem is especially challenging due to the high problem dimension and perturbing accelerations that prevent or complicate accurate analytical solutions. This analysis seeks to simplify the calculation of the nonaveraged spiral trajectory through the use of the well-known Q-Law guidance algorithm. Here, Q-Law is used to seed phases of the direct trajectory optimization problem. We explore the trade space between the fast calculation speed of Q-Law and the time or mass optimality of the full optimization problem using the common example of a geostationary transfer orbit to geostationary transfer. We find that a computationally efficient, near-optimal solution can be achieved by using Q-Law for an initial fraction of a spiral trajectory and direct optimization for the remainder of the trajectory. This reduces the direct optimization problem to a lower dimension and enables the spacecraft to reach a specific final state. Q-Law is particularly effective for portions of the trajectory where there are many eclipses, which can challenge direct optimization methods.

Direct method for uncertain multi-objective optimization based on interval non-dominated sorting

The interval optimization methods which describe the uncertainty by intervals are widely used in uncertain multi-objective optimization. Commonly, the interval values of the objective functions are substituted by approximate values, which will cause the loss of accuracy. To deal with the problem, a direct method is presented in this paper. In the framework of the multi-objective genetic algorithm, the upper and lower boundaries of the objective and constraint functions are found using the Monte Carlo stochastic simulation method and the constraints are handled by the degree of interval constraint violation; and then every two individuals from the combination population of the evolutionary population and the external elite population are compared using the interval comparison method. Afterwards, an interval non-dominated sorting based on the interval dominance relations is performed to sort the combination population into different non-dominated level. Furthermore, a general crowding distance is calculated for each individual to make individuals from the same non-dominated level comparable and also to maintain the diversity. The efficiency and accuracy of the proposed method is demonstrated by three test functions, the multi-objective structural optimization of the ten-bar truss, and the multi-objective structural optimization of a vehicle body for crashworthiness and lightweight.

Learning Direct Optimization for scene understanding

We develop a Learning Direct Optimization (LiDO) method for the refinement of a latent variable model that describes input image x. Our goal is to explain a single image x with an interpretable 3D computer graphics model having scene graph latent variables z (such as object appearance, camera position). Given a current estimate of z we can render a prediction of the image g(z), which can be compared to the image x. The standard way to proceed is then to measure the error E(x, g(z)) between the two, and use an optimizer to minimize the error. However, it is unknown which error measure E would be most effective for simultaneously addressing issues such as misaligned objects, occlusions, textures, etc. In contrast, the LiDO approach trains a Prediction Network to predict an update directly to correct z, rather than minimizing the error with respect to z. Experiments show that LiDO converges rapidly as it does not need to perform a search on the error landscape, produces better solutions than error-based competitors, and is able to handle the mismatch between the data and the fitted scene model. We apply LiDO to a realistic synthetic dataset, and show that the method also transfers to work well with real images.

Predictive Forward Dynamic Simulation of Manual Wheelchair Propulsion on a Rolling Dynamometer.

Research studies to understand the biomechanics of manual wheelchair propulsion often incorporate experimental data and mathematical models. This project aimed to advance this field of study by developing a two-dimensional (2D) model to generate first of its kind forward dynamic fully predictive computer simulations of a wheelchair basketball athlete on a stationary ergometer. Subject-specific parameters and torque generator functions were implemented in the model from dual X-ray absorptiometry and human dynamometer measurements. A direct collocation optimization method was used in a wheelchair propulsion model for the first time to replicate the human muscle recruitment strategy. Simulations were generated for varying time constraints and seat positions. Similar magnitudes of kinematic and kinetic data were observed between simulation and experimental data of a first push. Furthermore, seat heights inferior to the neutral position were found to produce similar joint torques to those reported in previous studies. An anterior seat placement produced the quickest push time with the least amount of shoulder torque required. The work completed in this project demonstrates that fully predictive simulations of wheelchair propulsion have the potential of varying simulation parameters to draw meaningful conclusions.

Airfoil–slat arrangement model design for wind turbines in fuzzy environment

In this study, a multi-element wind turbine blade that consists of NACA 6411 and NACA 4412 leading-edge slat design is investigated computationally. Optimum design parameters of the slatted wind turbine blade leading to maximum value of CL/CD related to the turbine power are obtained. In the optimization process, a new fuzzy logic linear programming methodology integrating with fuzzy linear regression and 2D CFD analysis is proposed. The aerodynamic characteristics of the slatted blade are computed by using Incompressible Navier–Stokes equations and k-omega turbulence modeling. Results are compared with the results of linear programming method and direct search optimization method. The computational results reveal that the proposed methodology for performance optimization is more effective than other methods to obtain high-performance value of the CL/CD. The maximum value of the CL/CD is obtained as 25.1 leading the maximum efficiency of 0.52.

Optimum design and performance analysis of heat exchanger coupling a flash dryer and parabolic trough collectors

Responding to the climate change issue, the deployment of thermal solar energy has grown remarkably. However, its use for industrial applications remains limited due to techno-economic constraints, among which the choice and optimum design of the heat exchanger allowing a profitable integration. In this context, the design of a crimped spiral fin-tube heat exchanger (CSFTHX) used to couple parabolic trough collectors and flash dryer was conducted. For this purpose, a mathematical model of CSFTHX was developed based on (ε-NTU) method and fitted to experimental data obtained in this work. The sensitivity of the model to geometrical parameters and operating variables was evaluated which results permitted to qualitatively validate this model and identify the optimum ranges of key design parameters. Then, the optimal design was carried out applying the conjugate direction optimization method considering the minimization of total annual cost as the objective function. Results showed that, at low Reynolds number (<1000), all geometrical parameters presented a significant effect on the HX thermal and hydraulic performances. Regarding the operating variables, the oil temperature and airflow rate had the most important impact on the HX required area, thus conducting to define the design point. The HX optimum design was achieved with a 20% lowered annual cost and 44% improved HX thermal performance. The designed HX was integrated within a bench scale solar flash dryer and the effect of the solar radiation intensity on the drying conditions was investigated, showing the necessity to use the back-up heating and avoid functioning under broken-clouds.

Separating two species of microalgae in photobioreactors in minimal time

This paper proposes a strategy to separate two strains of microalgae in minimal time. The control is the dilution rate of the continuous photobioreactor. The microalgae dynamics is described by the Droop’s model, taking into account the internal quota storage of the cells. Using Pontryagin’s principle, we develop a dilution-based control strategy that leads to the most efficient species separation in minimal time. A numerical optimal synthesis –based on direct optimization methods– is performed throughout the paper, in order to determine the structure of the optimal feedback-control law, which is bang-singular. Our numerical study reveals that singular arcs play a key role in the optimization problem since they allow the optimal solution to be close to an associated static optimal control problem. A resulting turnpike-like behavior, which characterizes the optimal solution, is highlighted throughout this work.

Well Placement Technique and Production Optimization for Mature Field - A Case Study of L-X Field

A Well placement is a well-known technique in the oil and gas industry for production optimization and are generally classified into local and global methods. The use of simulation software often deployed under the direct optimization technique called global method. The production optimization of L-X field which is at primary recovery stage having five producing wells was the focus of this work. The attempt was to optimize L-X field using a well placement technique.The local methods are generally very efficient and require only a few forward simulations but can get stuck in a local optimal solution. The global methods avoid this problem but require many forward simulations. With the availability of simulator software, such problem can be reduced thus using the direct optimization method. After optimization an increase in recovery factor of over 20% was achieved. The results provided an improvement when compared with other existing methods from the literatures.

Variational calculations of excited states via direct optimization of the orbitals in DFT.

A direct optimization method for obtaining excited electronic states using density functionals is presented. It involves selective convergence on saddle points on the energy surface representing the variation of the energy as a function of the electronic degrees of freedom, thereby avoiding convergence to a minimum and corresponding variational collapse to the ground electronic state. The method is based on an exponential transformation of the molecular orbitals, making it possible to use efficient quasi-Newton optimization approaches. Direct convergence on a target nth-order saddle point is guided by an appropriate preconditioner for the optimization as well as the maximum overlap method. Results of benchmark calculations of 52 excited states of molecules indicate that the method is more robust than a standard self-consistent field (SCF) approach especially when degenerate or quasi-degenerate orbitals are involved. The method can overcome challenges arising from rearrangement of closely spaced orbitals in a charge-transfer excitation of the nitrobenzene molecule, a case where the SCF fails to converge. The formulation of the method is general and can be applied to non-unitary invariant functionals, such as self-interaction corrected functionals.

Overview of Optimality of New Direct Optimal Methods for the Transportation Problems

In this paper, we investigate the claimed optimality of a new method – Revised Distribution (RDI) Method – for finding optimal solution of balanced and unbalanced transportation models directly and compare the RDI method with other such methods. A large set of problems have been tested by RDI and other methods, and the results were compared with the Modified distribution (MODI) method – an optimal method. We found that the mostly the results of RDI are not optimal. For reference to prove our observations, we have added three example transportation problems here in this work and compared their results with MODI method to show that the RDI method like the direct exponential approach (DEA) method is not optimal method; but it is just an initial basic feasible solution (IBFS) for transportation problems.