Aperture shape optimization in intensity-modulated radiation therapy planning

The gradient element of the aperture gradient map is utilized directly to generate the aperture shape without modulation.This process can be likened to choosing the direction of negative gradient descent for the generic aperture shape optimiza-tion.The negative gradient descent direction is more suitable under local conditions and has a slow convergence rate.To overcome these limitations,this study introduced conjugate gradients into aperture shape optimization based on gradient modulation.First,the aperture gradient map of the current beam was obtained for the proposed aperture shape optimiza-tion method,and the gradients of the aperture gradient map were modulated using conjugate gradients to form a modulated gradient map.The aperture shape was generated based on the modulated gradient map.The proposed optimization method does not change the optimal solution of the original optimization problem,but changes the iterative search direction when generating the aperture shape.The performance of the proposed method was verified using cases of head and neck cancer,and prostate cancer.The optimization results indicate that the proposed optimization method better protects the organs at risk and rapidly reduces the objective function value by ensuring a similar dose distribution to the planning target volume.Compared to the contrasting methods,the normal tissue complication probability obtained by the proposed optimization method decreased by up to 4.61%,and the optimization time of the proposed method decreased by 5.26%on average for ten cancer cases.The effectiveness and acceleration of the proposed method were verified through comparative experiments.According to the comparative experiments,the results indicate that the proposed optimization method is more suitable for clinical applications.It is feasible for the aperture shape optimization involving the proposed method.

CAD APPROACH FOR PLASTIC MOULD PARTING DIRECTIONS OPTIMIZATION

A CAD approach which can optimize and automate the parting direction determination is presented. The approach is based on the geometrical and topological information of the solid modelling of the plastic moulded part in order to select a pair of optimal parting directions of a two plate mould which minimizes the number of side cores. The shell of a part is divided into inter influential regions and non influential faces in the mould design point of view. Through analyzing and computing the accessibility direction cones of the inter influential regions, the optimal parting directions can be determined automatically.

Radial Basis Function Interpolation and Galerkin Projection for Direct Trajectory Optimization and Costate Estimation

This work presents a novel approach combining radial basis function(RBF)interpolation with Galerkin projection to efficiently solve general optimal control problems.The goal is to develop a highly flexible solution to optimal control problems,especially nonsmooth problems involving discontinuities,while accounting for trajectory accuracy and computational efficiency simultaneously.The proposed solution,called the RBF-Galerkin method,offers a highly flexible framework for direct transcription by using any interpolant functions from the broad class of global RBFs and any arbitrary discretization points that do not necessarily need to be on a mesh of points.The RBF-Galerkin costate mapping theorem is developed that describes an exact equivalency between the Karush-Kuhn-Tucker(KKT)conditions of the nonlinear programming problem resulted from the RBF-Galerkin method and the discretized form of the first-order necessary conditions of the optimal control problem,if a set of discrete conditions holds.The efficacy of the proposed method along with the accuracy of the RBF-Galerkin costate mapping theorem is confirmed against an analytical solution for a bang-bang optimal control problem.In addition,the proposed approach is compared against both local and global polynomial methods for a robot motion planning problem to verify its accuracy and computational efficiency.

Optimal control of stretching process of flexible solar arrays on spacecraft based on a hybrid optimization strategy

The optimal control of multibody spacecraft during the stretching process of solar arrays is investigated,and a hybrid optimization strategy based on Gauss pseudospectral method（GPM） and direct shooting method（DSM） is presented. First, the elastic deformation of flexible solar arrays was described approximately by the assumed mode method, and a dynamic model was established by the second Lagrangian equation. Then, the nonholonomic motion planning problem is transformed into a nonlinear programming problem by using GPM. By giving fewer LG points, initial values of the state variables and control variables were obtained. A serial optimization framework was adopted to obtain the approximate optimal solution from a feasible solution. Finally, the control variables were discretized at LG points, and the precise optimal control inputs were obtained by DSM. The optimal trajectory of the system can be obtained through numerical integration. Through numerical simulation, the stretching process of solar arrays is stable with no detours, and the control inputs match the various constraints of actual conditions.The results indicate that the method is effective with good robustness.

Low-thrust trajectory optimization for multiple target bodies tour mission

Spacecraft science missions to planets or asteroids have historically visited only one or several celestial bodies per mission.The research goal of this paper is to create a trajectory design algorithm that generates trajectory allowing a spacecraft to visit a significant number of asteroids during a single mission.For the problem of global trajectory optimization,even with recent advances in low-thrust trajectory optimization,a full enumeration of this problem is not possible.This work presents an algorithm to traverse the searching space in a practical fashion and generate solutions.The flight sequence is determined in ballistic scenario,and a differential evolution method is used with constructing a three-impulse transfer problem,then the local optimization is implemented with low-thrust propulsion on the basis of the solutions of impulsive trajectories.The proposed method enables trajectory design for multiple asteroids tour by using available low thrust propulsion technology within fuel and time duration constraints.

Robust multi-objective optimization of rolling schedule for tandem cold rolling based on evolutionary direction differential evolution algorithm

According to the actual requirements,profile and rolling energy consumption are selected as objective functions of rolling schedule optimization for tandem cold rolling.Because of mechanical wear,roll diameter has some uncertainty during the rolling process,ignoring which will cause poor robustness of rolling schedule.In order to solve this problem,a robust multi-objective optimization model of rolling schedule for tandem cold rolling was established.A differential evolution algorithm based on the evolutionary direction was proposed.The algorithm calculated the horizontal angle of the vector,which was used to choose mutation vector.The chosen vector contained converging direction and it changed the random mutation operation in differential evolution algorithm.Efficiency of the proposed algorithm was verified by two benchmarks.Meanwhile,in order to ensure that delivery thicknesses have descending order like actual rolling schedule during evolution,a modified Latin Hypercube Sampling process was proposed.Finally,the proposed algorithm was applied to the model above.Results showed that profile was improved and rolling energy consumption was reduced compared with the actual rolling schedule.Meanwhile,robustness of solutions was ensured.

DOA estimation via sparse recovering from the smoothed covariance vector

A direction of arrival（DOA） estimation algorithm is proposed using the concept of sparse representation. In particular, a new sparse signal representation model called the smoothed covariance vector（SCV） is established, which is constructed using the lower left diagonals of the covariance matrix. DOA estimation is then achieved from the SCV by sparse recovering, where two distinguished error limit estimation methods of the constrained optimization are proposed to make the algorithms more robust. The algorithm shows robust performance on DOA estimation in a uniform array, especially for coherent signals. Furthermore, it significantly reduces the computational load compared with those algorithms based on multiple measurement vectors（MMVs）. Simulation results validate the effectiveness and efficiency of the proposed algorithm.

An adaptive beamforming algorithm based on direction vector rotation and joint iterative optimization

An adaptive beamforming algorithm named robust joint iterative optimizationdirection adaptive （RJIO-DA） is proposed for large-array scenarios. Based on the framework of minimum variance distortionless response （MVDR）, the proposed algorithm jointly updates a transforming matrix and a reduced-rank filter. Each column of the transforming matrix is treated as an independent direction vector and updates the weight values of each dimension within a subspace. In addition, the direction vector rotation improves the performance of the algorithm by reducing the uncertainties due to the direction error. Simulation results show that the RJIO-DA algorithm has lower complexity and faster convergence than other conventional reduced-rank algorithms.

Nonparametric Probabilistic Prediction of Regional PV Outputs Based on Granule-based Clustering and Direct Optimization Programming

Regional photovoltaic(PV) power prediction plays an important role in power system planning and operation. To effectively improve the performance of prediction intervals(PIs) for very short-term regional PV outputs, an efficient nonparametric probabilistic prediction method based on granulebased clustering(GC) and direct optimization programming(DOP) is proposed. First, GC is proposed to formulate and cluster the sample granules consisting of numerical weather prediction(NWP) and historical regional output data, for the enhanced hierarchical clustering performance. Then, to improve the accuracy of samples' utilization, an unbalanced extension is used to reconstruct the training samples consisting of power time series. After that, DOP is applied to quantify the output weights based on the optimal overall performance. Meanwhile, a balance coefficient is studied for the enhanced reliability of PIs. Finally, the proposed method is validated through multistep PIs based on the numerical comparison of real PV generation data.

Direct aperture optimization based on genetic algorithm and conjugate gradient in intensity modulated radiation therapy

For resolving the problem that a conventional intensity modulated radiotherapy （IMRT） plan designed with the ＂two-step method＂-creates a greater number of apertures and total Monitor Units （MU）, the direct aperture optimization （DAO） method using a genetic algorithm and conjugate gradient was studied based on Accurate/ Advanced Radiation Therapy System （ARTS） developed by the FDS Team （www.fds.org.cn）.

A fault-tolerant triple-redundant voice coil motor for direct drive valves:Design, optimization, and experiment

A direct drive actuator （DDA） with direct drive valves （DDVs） as the control device is an ideal solution for a flight actuation system. This paper presents a novel triple-redundant voice coil motor （TRVCM） used for redundant DDVs. The TRVCM features electrical/mechanical hybrid triple-redundancy by securing three stators along with three moving coils in the same frame. A permanent magnet （PM） Halbach array is employed in each redundant VCM to simplify the system structure. A back-to-back design between neighborly redundancies is adopted to decouple the magnetic flux linkage. The particle swarm optimization （PSO） method is implemented to optimize design parameters based on the analytical magnetic circuit model. The optimization objective function is defined as the acceleration capacity of the motor to achieve high dynamic performance. The optimal geometric parameters are verified with 3D magnetic field finite element analysis （FEA）. A research prototype has been developed for experimental purpose. The experimental results of magnetic field density and force output show that the proposed TRVCM has great potential of applications in DDA systems.

Reentry Trajectory Optimization for Hypersonic Vehicles Using Fuzzy Satisfactory Goal Programming Method

Constrained reentry trajectory optimization for hypersonic vehicles is a challenging job. In particular, this problem becomes more difficult when several objectives with preemptive priorities are expected for different purposes. In this paper, a fuzzy satisfactory goal programming method is proposed to solve the multi-objective reentry trajectory optimization problem. Firstly, direct collocation approach is used to discretize the reentry trajectory optimal-control problem with nonlinear constraints into nonlinear multiobjective programming problem with preemptive priorities, where attack angles and bank angles at nodes and collocation nodes are selected as control variables. Secondly, the preemptive priorities are transformed into the relaxed order of satisfactory degrees according to the principle that the objective with higher priority has higher satisfactory degree. Then the fuzzy satisfactory goal programming model is proposed. The balance between optimization and priorities is realized by regulating parameter λ, such that the satisfactory reentry trajectory can be acquired. The simulation demonstrates that the proposed method is effective for the multi-objective reentry trajectory optimization of hypersonic vehicles.

A NONMONOTONE SECOND-ORDER STEPLENGTH METHOD FOR UNCONSTRAINED MINIMIZATION

In this paper, a nonmonotone method based on McCormick＇s second-order Armijo＇s step-size rule [7] for unconstrained optimization problems is proposed. Every limit point of the sequence generated by using this procedure is proved to be a stationary point with the second-order optimality conditions. Numerical tests on a set of standard test problems are presented and show that the new algorithm is efficient and robust.

High-voltage output triboelectric nanogenerator with DC/AC optimal combination method

The high-voltage power source is one of the important research directions of triboelectric nanogenerator(TENG).In this paper,a high-voltage output TENG(HVO-TENG)is proposed with direct current/alternating current(DC/AC)optimal combination method for wind energy harvesting.Through the optimal design of a direct current generation unit(DCGU)and an alternating current generation unit(ACGU),the HVO-TENG can produce DC voltage of 21.5 kV and AC voltage of 200 V,simultaneously.The HVOTENG can continuously illuminate more than 6,000 light emitting diodes(LEDs),which is enough to drive more possible applications of TENG.Besides,this paper explored application experiments on HVO-TENG.Demonstrative experiments indicate that the high-voltage DC output is used for producing ozone,while the AC output can light up ultraviolet(UV)LEDs.The HVOTENG can increase the ozone concentration(C)in an airtight container to 3 parts per million(ppm)after 7 h and continuously light up UV LEDs.All these demonstrations verify that the HVO-TENG has important guiding significance for designing high performance TENG.

Direct-to-indirect mapping for optimal low-thrust trajectories

Optimal,many-revolution spacecraft trajectories are challenging to solve.A connection is made for a class of models between optimal direct and indirect solutions.For transfers that minimize thrust-acceleration-squared,primer vector theory maps direct,many-impulsive-maneuver trajectories to the indirect,continuous-thrust-acceleration equivalent.The mapping algorithm is independent of how the direct solution is obtained and requires only a solver for a boundary value problem and its partial derivatives.A Lambert solver is used for the two-body problem in this work.The mapping is simple because the impulsive maneuvers and co-states share the same linear space around an optimal trajectory.For numerical results,the direct coast-impulse solutions are demonstrated to converge to the indirect continuous solutions as the number of impulses and segments increases.The two-body design space is explored with a set of three many-revolution,many-segment examples changing semimajor axis,eccentricity,and inclination.The first two examples involve a small change to either semimajor axis or eccentricity,and the third example is a transfer to geosynchronous orbit.Using a single processor,the optimization runtime is seconds to minutes for revolution counts of 10 to 100,and on the order of one hour for examples with up to 500 revolutions.Any of these thrust-acceleration-squared solutions are good candidates to start a homotopy to a higher-fidelity minimization problem with practical constraints.