Anti-interference beam pattern design based on second-order cone programming optimization

When signal-to-interference ratio is low, the energy of strong interference leaked from the side lobe of beam pattern will infect the detection of weak target. Therefore, the beam pattern needs to be optimized. The existing Dolph-Chebyshev weighting method can get the lowest side lobe level under given main lobe width, but for the other non-uniform circular array and nonlinear array, the low side lobe pattern needs to be designed specially. The second order cone programming optimization （SOCP） algorithm proposed in the paper transforms the optimization of the beam pattern into a standard convex optimization problem. Thus there is a paradigm to follow for any array formation, which not only achieves the purpose of Dolph-Chebyshev weighting, but also solves the problem of the increased side lobe when the signal is at end fire direction The simulation proves that the SOCP algorithm can detect the weak target better than the conventional beam forming.

Improved design of reconfigurable frequency response masking filters based on second-order cone programming

In order to improve the design results for the reconfigurable frequency response masking FRM filters an improved design method based on second-order cone programming SOCP is proposed.Unlike traditional methods that separately design the proposed method takes all the desired designing modes into consideration when designing all the subfilters. First an initial solution is obtained by separately designing the subfilters and then the initial solution is updated by iteratively solving a SOCP problem. The proposed method is evaluated on a design example and simulation results demonstrate that jointly designing all the subfilters can obtain significantly lower minimax approximation errors compared to the conventional design method.

AN INFEASIBLE-INTERIOR-POINT PREDICTOR-CORRECTOR ALGORITHM FOR THE SECOND-ORDER CONE PROGRAM

A globally convergent infeasible-interior-point predictor-corrector algorithm is presented for the second-order cone programming （SOCP） by using the Alizadeh- Haeberly-Overton （AHO） search direction. This algorithm does not require the feasibility of the initial points and iteration points. Under suitable assumptions, it is shown that the algorithm can find an -approximate solution of an SOCP in at most O（√n ln（ε0/ε）） iterations. The iteration-complexity bound of our algorithm is almost the same as the best known bound of feasible interior point algorithms for the SOCP.

Two new predictor-corrector algorithms for second-order cone programming

Based on the ideas of infeasible interior-point methods and predictor-corrector algorithms, two interior-point predictor-corrector algorithms for the second-order cone programming （SOCP） are presented. The two algorithms use the Newton direction and the Euler direction as the predictor directions, respectively. The corrector directions belong to the category of the Alizadeh-Haeberly-Overton （AHO） directions. These algorithms are suitable to the cases of feasible and infeasible interior iterative points. A simpler neighborhood of the central path for the SOCP is proposed, which is the pivotal difference from other interior-point predictor-corrector algorithms. Under some assumptions, the algorithms possess the global, linear, and quadratic convergence. The complexity bound O（rln（εo/ε）） is obtained, where r denotes the number of the second-order cones in the SOCP problem. The numerical results show that the proposed algorithms are effective.

Robust Blind Separation for MIMO Systems against Channel Mismatch Using Second-Order Cone Programming

To improve the deteriorated capacity gain and source recovery performance due to channel mismatch problem,this paper reports a research about blind separation method against channel mismatch in multiple-input multiple-output(MIMO) systems.The channel mismatch problem can be described as a channel with bounded fluctuant errors due to channel distortion or channel estimation errors.The problem of blind signal separation/extraction with channel mismatch is formulated as a cost function of blind source separation(BSS) subject to the second-order cone constraint,which can be called as second-order cone programing optimization problem.Then the resulting cost function is solved by approximate negentropy maximization using quasi-Newton iterative methods for blind separation/extraction source signals.Theoretical analysis demonstrates that the proposed algorithm has low computational complexity and improved performance advantages.Simulation results verify that the capacity gain and bit error rate(BER) performance of the proposed blind separation method is superior to those of the existing methods in MIMO systems with channel mismatch problem.

Feasibility and Structural Feature on Monotone Second-Order Cone Linear Complementarity Problems in Hilbert Space

Given a real finite-dimensional or infinite-dimensional Hilbert space H with a Jordan product, the second-order cone linear complementarity problem(SOCLCP)is considered. Some conditions are investigated, for which the SOCLCP is feasible and solvable for any element q?H. The solution set of a monotone SOCLCP is also characterized. It is shown that the second-order cone and Jordan product are interconnected.

Dose Distributions in Simulated Electron Radiotherapy with Intraoral Cones Using Treatment Planning System

Aim: This study aims to evaluate the difference between depth data from an intraoral cone and a conventional irradiation tube calculated using a treatment planning system (TPS), and that measured using an intraoral cone for electron radiotherapy. Background: A TPS is only compatible with conventional irradiation tubes. However, such systems are not suitable for determining dose distributions when a special cone is employed. Materials and Methods: Dose distributions were calculated using the beam data for mounted intraoral cones using a TPS. Then, the dose distribution by field size was calculated for a low-melting-point lead alloy using the beam data for a mounted conventional tube. The calculated data were evaluated against the measured intraoral-cone depth data based on the dose and depth differences. Results: The calculated data for the intraoral cone case did not match the measured data. However, the depth data obtained considering the field size determined for the lead alloy using the conventional tube were close to the measured values for the intraoral cone case. The difference in the depth at which the absorbed dose was 50% of the maximum value of the percentage depth dose was less than ±4 mm for the generalized Gaussian pencil beam convolution algorithm and less than ±1 mm for the electron Monte Carlo algorithm. Conclusion: It was found that the measured and calculated dose distributions were in agreement, especially when then electron Monte Carlo algorithm was used. Thus, the TPS can be employed to determine dose distributions for intraoral cone applications.

A VU-decomposition method for a second-order cone programming problem

A vu-decomposition method for solving a second-order cone problem is presented in this paper. It is first transformed into a nonlinear programming problem. Then, the structure of the Clarke subdifferential corresponding to the penalty function and some results of itsvu-decomposition are given. Under a certain condition, a twice continuously differentiable trajectory is computed to produce a second-order expansion of the objective function. A conceptual algorithm for solving this problem with a superlinear convergence rate is given.

Method for Converting Cone-Beam CT Values into Hounsfield Units for Radiation Treatment Planning

Cone-beam CT (CBCT) images acquired during radiation treatment can be used to recalculate the dose distribution as well as to confirm the treatment location. However, it is difficult to obtain the electron densities (EDs) necessary for dose calculation from CBCT images because of the effects of scatter contamination during CBCT image acquisition. This paper presents a mathematical method for converting the pixel values of CBCT images (CBCT values) into Hounsfield units (HUs) of radiation treatment simulation CT (simCT) images for use in radiation treatment planning. CBCT values are converted into HUs by matching the histograms of the CBCT values with the histograms of the HUs for each slice via linear scaling of the CBCT values. For prostate cancer and head-and-neck cancer patients, the EDs obtained from converted CBCT values (mCBCT values) show good agreement with the EDs obtained from HUs, within approximately 3.0%, and the dose calculated on the basis of CBCT images shows good agreement with the dose calculated on the basis of the simCT images, within approximately 2.0%. Because the CBCT values are converted for each slice, this conversion method can account for variation in the CBCT values associated with differences in body size, body shape, and inner tissue structures, as well as in longitudinally displaced positions from the isocenter, unlike conventional methods that use electron density phantoms. This method improves on conventional CBCT-ED conversion and shows considerable potential for improving the accuracy of radiation treatment planning using CBCT images.

POSITIVE SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR SECOND-ORDER SINGULAR NONLINEAR DIFFERENTIAL EQUATIONS

New existence results are presented for the singular second-order nonlinear boundary value problems u ' + g(t)f(u) = 0, 0 < t < 1, au(0) - betau ' (0) = 0, gammau(1) + deltau ' (1) = 0 under the conditions 0 less than or equal to f(0)(+) < M-1, m(1) < f(infinity)(-)less than or equal to infinity or 0 less than or equal to f(infinity)(+)< M-1, m(1) < f (-)(0)less than or equal to infinity where f(0)(+) = lim(u -->0)f(u)/u, f(infinity)(-)= lim(u --> infinity)f(u)/u, f(0)(-)= lim(u -->0)f(u)/u, f(infinity)(+) = lim(u --> infinity)f(u)/u, g may be singular at t = 0 and/or t = 1. The proof uses a fixed point theorem in cone theory.

Novel algorithm of gait planning of hydraulic quadruped robot to avoid foot slidingand reduce impingement

In order to solve kinematic redundancy problems of a hydraulic quadruped walking robot,which include leg dragging,sliding,impingement against the ground,an improved gait planning algorithm for this robot is proposed in this paper.First,the foot trajectory is designated as the improved composite cycloid foot trajectory.Second,the landing angle of each leg of the robot is controlled to satisfy friction cone to improve the stability performance of the robot.Then with the controllable landing angle of quadruped robot and a geometry method,the kinematic equation is derived in this paper.Finally,agait planning method of quadruped robot is proposed,a dynamic co-simulation is done with ADAMS and MATLAB,and practical experiments are conducted.The validity of the proposed algorithm is confirmed through the co-simulation and experimentation.The results show that the robot can avoid sliding,reduce impingement,and trot stably in trot gait.

Positive Solutions for a Class of Second-order m-point Boundary Value Problems

Using a fixed point theorem in cones, the paper consider the existence of positive solutions for a class of second-order m-point boundary value problem. Sufficient conditions to ensure the existence of double positive solutions are obtained. The associated Green function of this problem is also given.

计及电-气双向耦合的综合能源配电网优化重构

综合能源系统是实现电网、气网以及热网等多种能源系统深度融合,利用能量耦合互补等优势提升整个系统能源利用效率的有效形式。为提升综合能源系统优化运行能力,文章首先基于电转气技术与天然气发电技术,构建了的电-气双向耦合综合能源系统总体模型。进而考虑配电网重构技术(Distribution Network Reconfiguration Technology,DNR)中拓扑结构灵活可控这一特性,在配电子系统中引入开关变量、系统运行总费用最低这一目标函数及网络辐射状拓扑结构等约束,建立了配电子系统重构模型。从降低模型求解复杂性的角度,应用二阶锥松弛、乘积变量线性化及分段线性化等方法,将原始综合能源配电网重构非凸非线性模型转化为混合整数二阶锥规划(Mixed Integer Second-Order Cone Programming,MISOCP)问题求解。仿真结果表明,在电-气双向耦合的综合能源系统中应用配电网重构技术,能够降低综合能源系统运行费用,同时有效支撑了配电子系统电压与配气子系统气压。

考虑电压-无功调节的台区互联装置规划方法

伴随分布式能源广泛接入低压配电网,其对配电网运行灵活性和消纳能力的要求不断提高。利用低压柔性互联装置将独立运行的低压配电台区分区互联,避免传统电压调节和无功补偿装置频繁动作。考虑到柔性互联装置造价昂贵,协同传统电压-无功调节装置,文中提出低压柔性互联装置的选址定容规划方法。首先,分析低压柔性互联装置拓扑和运行方式,建立其潮流模型。其次,建立低压柔性互联装置优化配置的双层规划模型,上层规划以年综合费用最小为目标,下层规划考虑电压-无功协调控制时间序列模型,以运行成本和电压偏差最小为目标,基于粒子群优化算法和混合整数二阶锥规划算法交替求解,得出配电系统最优柔性互联方案和最优运行方式。最后,在IEEE 33节点系统上进行实例分析,验证该双层规划算法的有效性。结果表明,所提方法能有效减少柔性互联装置的过度布置,同时减少由分布式能源频繁波动造成的运行成本。将模型凸化并线性化的方法明显提高了求解效率。

A stable implicit nodal integration-based particle finite element method(N-PFEM)for modelling saturated soil dynamics

In this study,we present a novel nodal integration-based particle finite element method(N-PFEM)designed for the dynamic analysis of saturated soils.Our approach incorporates the nodal integration technique into a generalised Hellinger-Reissner(HR)variational principle,creating an implicit PFEM formulation.To mitigate the volumetric locking issue in low-order elements,we employ a node-based strain smoothing technique.By discretising field variables at the centre of smoothing cells,we achieve nodal integration over cells,eliminating the need for sophisticated mapping operations after re-meshing in the PFEM.We express the discretised governing equations as a min-max optimisation problem,which is further reformulated as a standard second-order cone programming(SOCP)problem.Stresses,pore water pressure,and displacements are simultaneously determined using the advanced primal-dual interior point method.Consequently,our numerical model offers improved accuracy for stresses and pore water pressure compared to the displacement-based PFEM formulation.Numerical experiments demonstrate that the N-PFEM efficiently captures both transient and long-term hydro-mechanical behaviour of saturated soils with high accuracy,obviating the need for stabilisation or regularisation techniques commonly employed in other nodal integration-based PFEM approaches.This work holds significant implications for the development of robust and accurate numerical tools for studying saturated soil dynamics.

RSS和AOA融合的单站低空无线电辐射源定位算法

提出一种在低空场景下基于接收信号强度(Rcecived Signal Strength,RSS)与到达角度(Angle of Arrival,AOA)信息融合的单站无源定位算法。该算法采用单架无人机设备虚拟多站设备接收无线电辐射源信号,融合RSS估计的距离信息与AOA方向角信息,依据最小二乘准则(LS)构造算法的优化目标函数,采用凸松弛技术将目标函数等价为二阶锥规划(SOCP)问题并通过内点法求解。实验结果表明,该算法的定位精度在2 km范围内可达20 m,其定位性能优于单站无源定位算法,且由于采用单架无人机采集信号,其设备复杂度相较于多站无源定位较低。

Collapsed Cone光子束剂量计算方法研究

剂量计算是放射治疗计划系统的核心,与常用的笔形束剂量计算方法相比,collapsed cone卷积/叠加剂量计算方法具有更高的计算精度,为此我们研究了collapsed cone卷积/叠加剂量计算方法及加速算法,开发了一套基于collapsed cone卷积/叠加剂量计算方法的光子束放射治疗计划系统,并运用蒙特卡罗方法对剂量计算的准确性进行了验证。实验结果表明剂量计算误差与射束能量、射野尺寸以及剂量计算分辨率有关,当天顶角增量和方位角增量分别取3.75°和15°时,对于3～20 cm的方野,剂量计算误差均小于1.5%。所开发的collapsed cone光子束剂量计算方法准确可靠,可望应用于临床。

一种基于MISOCP的复杂绕飞区轨迹优化方法

针对复杂绕飞问题,为提升优化方法的全局寻优能力,提出一种基于混合整数二阶锥规划(MISOCP)的迭代求解算法。首先,定量分析了传统序列凸化方法处理绕飞区(NFZ)约束产生的误差;随后,为消除误差,利用整数变量结合自变量变换将绕飞区约束转化为混合整数线性约束;最后,将原问题转化为MISOCP问题,并设计了迭代算法进行求解。仿真表明,本方法全局寻优能力强,且求解时间仅为GPOPS的20%。对随机生成的复杂绕飞场景,本方法鲁棒性较好,且平均求解时间在10 s量级。

基于二阶锥规划的配电网源-网-荷-储联合规划方法设计

随着高比例分布式光伏接入配电网,如何对线路进行规划与源-储定址定容成为无法避免的问题。提出了配电网源-网-荷-储双层联合扩展规划策略,上层以配电网系统网络年投资费用最小和网损惩罚费用最小为目标建立线路规划模型,实现对配电网线路走向的改进;下层针对源、荷的不确定性以配电网运行收益最大为目标建立配电网源-储定址定容模型,同时引入不确定性参数对源-荷不确定性集的范围进行约束。针对所建双层规划模型非线性、难求解问题,基于二阶锥松弛算法将上述非凸、非线性优化规划模型转换为二阶锥优化模型,进而获得全局最优解,以此得到分布式光伏以及储能的最佳接入位置和容量。仿真结果表明,该方法可有效降低配电网的规划成本,促进分布式电源的消纳。

Dispatchable Region for Active Distribution Networks Using Approximate Second-order Cone Relaxation

Uncertainty in distributed renewable generation threatens the security of power distribution systems.The concept of dispatchable region is developed to assess the ability of power systems to accommodate renewable generation at a given operating point.Although DC and linearized AC power flow equations are typically used to model dispatchable regions for transmission systems,these equations are rarely suitable for distribution networks.To achieve a suitable trade-off between accuracy and efficiency,this paper proposes a dispatchable region formulation for distribution networks using tight convex relaxation.Secondorder cone relaxation is adopted to reformulate AC power flow equations,which are then approximated by a polyhedron to improve tractability.Further,an efficient adaptive constraint generation algorithm is employed to construct the proposed dispatchable region.Case studies on distribution systems of various scales validate the computational efficiency and accuracy of the proposed method.