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.

THREE-DIMENSIONAL TRAJECTORY OPTIMIZATION WITH DIRECT METHOD

The principle of direct method used in optimal control problem is introduced. Details of applying this method to flight trajectory generation are presented including calculation of velocity and controls histories. And capabilities of flight and propulsion systems are considered also. Combined with digital terrain map technique, the direct method is applied to the three dimensional trajectory optimization for low altitude penetration, and simplex algorithm is used to solve the parameters in optimization. For the small number of parameters, the trajectory can be optimized in real time on board.

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.

Influence of Atmospheric Refraction on Horizontal Angle Surveying

Side-refraction is the main error source of horizontal angle surveying, but it has little influence on the sides by analyzing the influence of atmospheric-infraction on the ultrahigh-precision side and angle surveying. Choosing oriented direction is crucial to distance and angle measurement in triangulateration network. How to select the oriented direction during angle measurement is presented, and the means to check the quality of auto-surveying with Georobot is brought forward as well. At last some solutions to reduce the influence of side-refraction while disposing and surveying ultrahigh-precision triangulateration network are put forward.

A Direct Compensative Robust Optimal Control (DCROC) Law for Ship Straight-line Track-keeping

A linear quadratic optimal direct track-keeping control law was proposed based on first-order Nomoto nominal model. Furthermore, based on Lyapunov stabilized theory, considering parametric uncertainty from variations of ship speed and disturbances uncertain from wind, wave and sea current, a direct compensative robust optimal control (DCROC) law was developed. It can guarantee closed-loop system globally and uniformly converge to a remained set. High accuracy and robustness were achieved. By introducing some nonlinear blocks, closed-loop system achieves global and uniform asymptotical stableness. Numerical simulations on a Mariner Class ship are presented to validate the control law.

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.

Energy-Efficient Transceiver Design for Multi-Pair Two-Way Relay Systems

In this paper, we focus on energy-efficient transceiver and relay beamforming design for multi-pair two-way relay system. The multi-antenna users and the multi-antenna relay are considered in this work. Different from the existing works, the proposed algorithm is energy-efficient which is more applicable to the future green network. It considers both the sum-MSE problem and the power consumption problem for the users under the relay power constraint. Based on the optimal condition decomposition(OCD) method, the energy-efficient precoders at the users can be designed separately with limited information exchanged. The proposed relay beamforming algorithm is based on the alternative direction method of multipliers(ADMM) which has simpler iterative solution and enjoys good convergence. Simulation results demonstrate the performance of the proposed algorithms in terms of power consumption and MSE performance.

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.

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.

Dosimetric evaluation of CR, 3DCRT and two types of IMRT for breast cancer after conservative surgery

Objective: The purpose of this study was to compare the dose distribution and dose volume histogram (DVH) of the planning target volume (PTV) and organs at risk (OARs) among conventional radiation therapy (CR), three-dimensional conformal radiation therapy (3DCRT), two-step intensity-modulated radiation therapy (TS-IMRT) and direct machine parameter optimization intensity-modulated radiation therapy (DMPO-IMRT) after breast-conserving surgery. Methods: For each of 20 randomly chosen patients, 4 plans were designed using 4 irradiation techniques. The prescribed dose was 50 Gy/2 Gy/25 f, 95% of the planning target volume received this dose. The cumulated DVHs and 3D dose distributions of CR, 3DCRT, TS-IMRT and DMPO-IMRT plans were compared. Results: For the homogeneity indices, no statistically significant difference was observed among CR, 3DCRT, TS-IMRT and DMPO-IMRT while the difference of the conformality indices were statistically significant. With regard to the organs at risk, IMRT and 3DCRT showed a significantly fewer exposure dose to the ipsilateral lung than CR in the high-dose area while in the low-dose area, IMRT demonstrated a significant increase of exposure dose to ipsilateral lung, heart and contralateral breast compared with 3DCRT and CR. In addition, the monitor units (MUs) for DMPO-IMRT were approximately 26% more than those of TS-IMRT and the segments of the former were approximately 24% less than those of the latter. Conclusion: Compared with CR, 3DCRT and IMRT improved the homogeneity and conformity of PTV, reduced the irradiated volume of OARs in high dose area but IMRT increased the irradiated volume of OARs in low dose area. DMPO-IMRT plan has fewer delivery time but more MUs than TS-IMRT.

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.

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.

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.

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.

Venus round trip using solar sail

Trajectory optimization and simulation is performed for Venus round trip (VeRT) mission using solar sail propulsion. Solar gravity is included but atmospheric drag and shadowing effects are neglected in the planet-centered escape and capture stages. The spacecraft starts from the Geostationary orbit (GEt) at a predetermined time to prepare a good initial condition for the Earth-Venus transfer, although the launch window is not an issue for spacecraft with solar sails. The Earth-Venus phase and the return trip are divided into three segments. Two methods are adopted to maintain the mission trajectory for the VeRT mis- sion and then compared through a numerical simulation. According to the first approach, Planet-centered and heliocentric ma- neuvers are modeled using a set of blended analytical control laws instead of the optimal control techniques. The second pro- cedure is the Direct Attitude Angle Optimization in which the attitude angles of the solar sail are adopted as the optimization variables during the heliocentric transfer. Although neither of the two methods guarantees a globally optimal trajectory, they are more efficient and will produce a near-optimal solution if employed properly. The second method has produced a better result for the minimum-time transfer of the VeRT mission demonstrating the effectiveness of the methods in the preliminary design of the complex optimal interplanetary orbit transfers.

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.

A code-based approach for labeling in complex irregular regions

Labeling information in a complex irregular region is a useful procedure occurring frequently in sheet metal and the furniture industry which will be beneficial in parts management.A fast code-based labeler(FCBL) is proposed to accomplish this objective in this paper.The region is first discretized,and then encoded by the Freeman encoding technique for providing the 2D regional information by 1D codes with redundancies omitted.We enhance the encoding scheme to make it more suitable for our complex problem.Based on the codes,searching algorithms are designed and can be extended with customized constraints.In addition,by introducing a smart optimal direction estimation,the labeling speed and accuracy of FCBL are significantly improved.Experiments with a large range of real data gained from industrial factories demonstrate the stability and millisecond-level speed of FCBL.The proposed method has been integrated into a shipbuilding CAD system,and plays a very important role in ship parts labeling process.