基于次梯度的L1正则化Hinge损失问题求解研究

Hinge损失函数是支持向量机(support vector machines,SVM)成功的关键,L1正则化在稀疏学习的研究中起关键作用.鉴于两者均是不可导函数,高阶梯度信息无法使用.利用随机次梯度方法系统研究L1正则化项的Hinge损失大规模数据问题求解.首先描述了直接次梯度方法和投影次梯度方法的随机算法形式,并对算法的收敛性和收敛速度进行了理论分析.大规模真实数据集上的实验表明,投影次梯度方法对于处理大规模稀疏数据具有更快的收敛速度和更好的稀疏性.实验进一步阐明了投影阈值对算法稀疏度的影响.

平滑削边绝对偏离惩罚截断Hinge损失支持向量机的财务危机预报

针对传统支持向量机(SVM)分类存在对离群点敏感、支持向量(SV)个数多和分类面参数非稀疏的问题,提出了平滑削边绝对偏离(SCAD)惩罚截断Hinge损失SVM(SCAD-TSVM)算法,并将其用于构建财务预警模型,同时就该模型的求解设计了一个迭代更新算法。结合沪深股市A股制造业上市公司的财务数据进行实证分析,同时对比L1范数惩罚SVM、SCAD惩罚SVM和截断Hinge损失SVM(TSVM)构建的T-2和T-3模型,结果发现SCAD-TSVM构建的T-2和T-3模型都具有最好的稀疏性和最高的预报精度,而且其在不同训练样本数上的平均预测准确率都要比L1范数SVM(L1-SVM)、SCAD-SVM和TSVM算法的高。

基于Hinge损失函数的垂向全变差约束全波形反演

全波形反演可以为叠前深度偏移成像提供更高精度的速度模型,但该方法具有较强的非线性,对初始速度模型的依赖性较强,尤其是在实际应用中,地质条件复杂多变,速度变化不连续,增加了反演非线性程度,常常使反演陷入局部极小值,影响反演的精度.全变差约束在图像去噪领域应用广泛,属于非光滑约束,在去噪过程中能有效的保留图像的不连续界面和边缘信息.本文提出基于Hinge损失函数的垂向全变差约束全波形反演方法,在全变差约束的基础上,利用Hinge损失函数控制模型的更新方向,并使用原-对偶混合梯度算法进行求解,给出这一优化问题的迭代格式,有效提高了对地下不连续界面的重构精度,同时也降低反演对初始速度模型的依赖程度.数值算例证明:与常规全波形反演方法相比,基于全变差约束的全波形反演方法可以有效的重构速度模型中的不连续界面,尤其对高速体边缘的重构效果更明显,但该方法对初始速度模型的依赖性仍然较强;基于Hinge损失函数的垂向全变差约束全波形反演方法降低了对初始速度模型的依赖程度,可以从一个较差的初始模型通过循环迭代的方式最终得到同样精确的速度模型,较好的重构了高速体边缘和不连续界面.

一种求解截断Hinge损失的软阈值坐标下降算法

有效地减少支持向量数目能够提高分类器的鲁棒性和精确性,缩短支持向量机(support vector machine,SVM)的训练和测试时间.在众多稀疏算法中,截断Hinge损失方法可以显著降低支持向量的数目,但却导致了非凸优化问题.一些研究者使用CCCP(concave-convex procedure)方法将非凸问题转化为多阶段凸问题求解,不仅增加了额外计算量,而且只能得到局部最优解.为了弥补上述不足,提出了一种基于CCCP的软阈值坐标下降算法.用坐标下降方法求解CCCP子阶段凸问题,提高计算效率;对偶SVM中引入软阈值投影技巧,能够减少更多的支持向量数目,同时选择合适的正则化参数可消除局部最优解的不良影响,提高分类器的分类精度.仿真数据库、UCI数据库和大规模真实数据库的实验证实了所提算法正确性和有效性.

基于Rescaled Hinge损失函数的多子支持向量机

针对多分类学习模型性能会受异常值影响的问题,提出基于Rescaled Hinge损失函数的多子支持向量机(RHMBSVM)。首先,该方法通过引入有界、非凸的Rescaled Hinge损失函数来构建相应的优化问题;然后,利用共轭函数理论将优化问题作等价变换;最后,使用变量交替策略形成一个迭代算法来求解非凸优化问题,该方法在求解的过程中可自动调节每个样本点的惩罚权重,从而削弱了异常值对K个超平面的影响,增强了鲁棒性。使用5折交叉验证的方法进行数值实验,实验结果表明,在数据集无异常值的情况下,该方法的正确率比多子支持向量机(MBSVM)提升了1.11个百分点,比基于Rescaled Hinge损失函数的鲁棒支持向量机(RSVM-RHHQ)提升了0.74个百分点;在数据集有异常值的情况下,该方法的正确率比MBSVM提升了2.10个百分点,比RSVM-RHHQ提升了1.47个百分点。实验结果证明了所提方法在解决有异常值的多分类问题上的鲁棒性。

Topological and Shape Optimization of Flexure Hinges for Designing Compliant Mechanisms Using the Level Set Method

A flexure hinge is a major component in designing compliant mechanisms that o ers unique possibilities in a wide range of application fields in which high positioning accuracy is required. Although various flexure hinges with di erent configurations have been successively proposed, they are often designed based on designers' experiences and inspirations. This study presents a systematic method for topological optimization of flexure hinges by using the level set method. Optimization formulations are developed by considering the functional requirements and geometrical constraints of flexure hinges. The functional requirements are first constructed by maximizing the compliance in the desired direction while minimizing the compliances in the other directions. The weighting sum method is used to construct an objective function in which a self-adjust method is used to set the weighting factors. A constraint on the symmetry of the obtained configuration is developed. Several numerical examples are presented to demonstrate the validity of the proposed method. The obtained results reveal that the design of a flexure hinge starting from the topology level can yield more choices for compliant mechanism design and obtain better designs that achieve higher performance.

Design and Experiment of Triangular Prism Mast with Tape-Spring Hyperelastic Hinges

Because of the limited space of the launch rockets, deployable mechanisms are always used to solve the phenomenon. One dimensional deployable mast can deploy and support antenna, solar sail and space optical camera. Tape-spring hyperelastic hinges can be folded and extended into a rod like configuration. It utilizes the strain energy to realize self-deploying and drive the other structures. One kind of triangular prism mast with tape-spring hyperelastic hinges is proposed and developed. Stretching and compression stiffness theoretical model are established with considering the tape-spring hyperelastic hinges based on static theory. The finite element model of ten-module triangular prism mast is set up by ABAQUS with the tape-spring hyperelastic hinge and parameter study is performed to investigate the influence of thickness, section angle and radius. Two-module TPM is processed and tested the compression stiffness by the laser displacement sensor, deploying repeat accuracy by the high speed camera, modal shape and fundamental frequency at cantilever position by LMS multi-channel vibration test and analysis system, which are used to verify precision of the theoretical and finite element models of ten-module triangular prism mast with the tape-spring hyperelastic hinges. This research proposes an innovative one dimensional triangular prism with tape-spring hyperelastic hinge which has great application value to the space deployable mechanisms.

Optimizing the Qusai-static Folding and Deploying of Thin-Walled Tube Flexure Hinges with Double Slots

The thin-walled tube flexure（TWTF） hinges have important potential application value in the deployment mechanisms of satellite and solar array, but the optimal design of the TWTF hinges haven＇t been completely solved, which restricts their applications. An optimal design method for the qusai-static folding and deploying of TWTF hinges with double slots is presented based on the response surface theory. Firstly, the full factorial method is employed to design of the experiments. Then, the finite element models of the TWTF hinges with double slots are constructed to simulate the qusai-static folding and deploying non-linear analysis. What＇s more, the mathematical model of the TWTF flexure hinge quasi-static folding and deploying properties are derived by the response surface method. Considering of small mass and high stability, the peak moment of quasi-static folding and deploying as well as the lightless are set as the objectives to get the optimal performances. The relative errors of the objectives between the optimal design results and the FE analysis results are less than 7%, which demonstrates the precision of the surrogate models. Lastly, the parameter study shows that both the slots length and the slots width both have significant effects to the peak moment of quasi-static folding and deploying of TWTF hinges with double slots. However, the maximum Mises stress of quasi-static folding is more sensitive to the slots length than the slots width. The proposed research can be applied to optimize other thin-walled flexure hinges under quasi-static folding and deploying, which is of great importance to design of flexure hinges with high stability and low stress.

Design and Test Analysis of a Solar Array Root Hinge Drive Assembly

A root hinge drive assembly is preferred in place of the classical viscous damper in a large solar array system.It has advantages including better deployment control and higher reliability.But the traditional single degree of freedom model should be improved.A multiple degrees of freedom dynamics model is presented for the solar arrays deployment to guide the drive assembly design.The established model includes the functions of the torsion springs,the synchronization mechanism and the lock-up impact.A numerical computation method is proposed to solve the dynamics coupling problem.Then considering the drive torque requirement calculated by the proposed model,a root hinge drive assembly is developed based on the reliability engineering design methods,and dual actuators are used as a redundancy design.Pseudo-efficiency is introduced and the major factors influencing the（pseudo-）efficiency of the gear mechanism designed with high reduction ratio are studied for further test data analysis.A ground prototype deployment test is conducted to verify the capacity of the drive assembly.The test device consists of a large-area solar array system and a root hinge drive assembly.The RHDA development time is about 43 s.The theoretical drive torque is compared with the test values which are obtained according to the current data and the reduction efficiency analysis,and the results show that the presented model and the calibration methods are proper enough.

Shear performance analysis of a heavy-duty universal hinged cast steel support

This paper presents the shear performance analysis of a heavy-duty universal hinged cast steel support with the largest bearing capacity. The effect of 9 parameters ( 52 specimens) ,i. e. height of the upper support,depth of the ring of the upper support,depth of the top plate of the bottom support,height of the ribs of the bottom support,depth of the ribs of the bottom support,bolt hole diameter,number of the ribs of the bowl,depth of the ribs of the bowl,and yield strength of the material,were analyzed with a 3-dimensional elastic-plastic finite element model in which the nonlinearities of geometry,material and contact were all considered. Analysis shows that height of the upper support,depth of the ring of the upper support and yield strength of the material have a great effect on the mechanical performance of the support. Height of the upper support has the largest effect on performance price ratio of the support,and the maximum effect can be up to 160% . Depth of the top plate of the bottom support,height of the ribs of the bottom support and depth of the ribs of the bottom support have a medium effect on performance price ratio of the support,and the effect is within the limit of 15% 19% .

A method to Estimate Dynamic Responses of VLFS Based on Multi-Floating-Module Model Connected by Elastic Hinges

Based on the elastic foundation beam theory and the multi-floating-module hydrodynamic theory,a novel method is proposed to estimate the dynamic responses of VLFS(Very Large Floating Structure).In still water,a VLFS can be simplified as an elastic foundation beam model or a multi-floating-module model connected by elastic hinges.According to equivalent displacement of the two models in static analysis,the problem of rotation stiffness of elastic hinges can be solved.Then,based on the potential flow theory,the dynamic responding analysis of multi-floatingmodule model under wave loads can be computed in ANSYS-AQWA software.By assembling the time domain analysis results of each module,the dynamic responses of the VLFS can be obtained.Validation of the method is conducted through a series of comparison calculations,which mainly includes a continuous structure and a three-part structure connected by hinges in regular waves.The results of this paper method show a satisfactory agreement with the experiment and calculation data given in relative references.

Analysis of the Micro-Rotation Compliant Mechanism Based on the Corner-Filleted Flexure Hinges

The purpose of this thesis is to derive the flexibility formula of the corner-filleted flexure hinge easily and conveniently and use it to design a micro-rotation compliant mechanism. Firstly,we get the corner-filleted flexure hinge flexibility formula by methods of symmetry transformation and coordinates translation. The correctness of this formula is validated on the basis of the finite element method and under the premise that the effects of shear stress are taken into consideration. Then a micro-rotation compliant mechanism is designed in accordance with the corner-filleted flexure hinge,and the deduction and analysis of its working moment/rigidity are conducted. Moreover,this theoretical formula is proved to be accurate and reliable through the finite element analysis and the experimental verification,based on which the structural design and optimization can be made on the rotating part of a micro adjustment device. The results illustrate that designing and optimizing the structures by the analysis model is convenient and reliable so that complicated 3D modeling and finite element analysis are not needed.

Numerical Modeling on Hydrodynamic Performance of A Bottom-Hinged Flap Wave Energy Converter

The hydrodynamic performance of a bottom-hinged flap wave energy converter （WEC） is investigated through a frequency domain numerical model. The numerical model is verified through a two-dimensional analytic solution, as well as the qualitative analysis on the dynamic response of avibrating system. The concept of ＂optimum density＂ of the bottom-hinged flap is proposed, and its analytic expression is derived as well. The frequency interval in which the optimum density exists is also obtained. The analytic expression of the optimum linear damping coefficient is obtained by a bottom-hinged WEC. Some basic dynamic properties involving natural period, excitation moment, pitch amplitude, and optimum damping coefficient are analyzed and discussed in detail. In addition, this paper highlights the analysis of effects on the conversion performance of the device exerted by some important parameters. The results indicate that ＂the optimum linear damping period of 5.0 s＂ is the most ideal option in the short wave sea states with the wave period below 6.0 s. Shallow water depth, large flap thickness and low flap density are advised in the practical design of the device in short wave sea states in order to maximize power capture. In the sea state with water depth of 5.0 m and wave period of 5.0 s, the results of parametric optimization suggest a flap with the width of 8.0 m, thickness of 1.6 m, and with the density as little as possible when the optimum power take-off （PTO） damping coefficient is adopted.

THE AUTOMATIC GENERATION OF LIMIT STATE FUNCTION OF HINGED STRUCTURE

In this paper, the theorem of structure continual variation of truss structure in the analysis of structure reliability is derived, and it is used to generate limit state function automatically. We can avoid repeated assembly of global stiffness matrix and repeated inverse operations of the matrix caused by constant changes of structure topology. A new criterion of degenerate of the structure into mechanism is introduced. The calculation examples are satisfactory.

Simulation optimal design of a compliant mechanism with circular notch flexure hinges based on the equivalent beam methodology

This paper presents an in-depth study of Equivalent beam model (EBM).Firstly three-dimensional (3D) finite element analysis (FEA) model for circular flexure hinge developed by Zettl et al.was verified by the comparison with Smith's experimental results and the 3D FEA model was feasible within 5.5% error.Then the accuracy of Timoshenko short-beam due to shear force was verified based on finite element method.The results showed that the EBM has good accuracy within 5% error for 1≤r/t≤3.Finally the EBM methodology was applied for the simulation optimal design of a bridge-type compliant mechanism.The results showed that the EBM methodology has very high numerical efficiency and satisfactory accuracy for simulation optimal design of planar compliant mechanism with flexure hinges.

Reliability Analysis of Flexure Hinge Based on Kriging Method

The uncertainty widely exists in the engineering practice.Therefore,it is necessary to research the effect of uncertainty on the structural system. In this paper,the reliability and sensitivity of the flexure hinge, which is the key component of the compliant mechanisms,are investigated. The results of the reliability analysis can effectively guide the engineer to design and optimize the flexure hinge. In order to improve the calculating efficiency,the kriging method is introduced to estimate the failure probability and reliability sensitivity.

Efficiency of employing fiber-based finite-length plastic hinges in simulating the cyclic and seismic behavior of steel hollow columns compared with other common modelling approaches

The accuracy and effi ciency of the modelling techniques utilized to model the nonlinear behavior of structural components is a signifi cant issue in earthquake engineering. In this study, the suffi ciency of three diff erent modelling techniques that can be employed to simulate the structural behavior of columns is investigated. A fi ber-based fi nite length plastic hinge (FB-FLPH) model is calibrated in this study. In order to calibrate the FB-FLPH model, a novel database of the cyclic behavior of hollow steel columns under simultaneous axial and lateral loading cycles with varying amplitudes is used. By employing the FB-FLPH model calibrated in this study, the interaction of the axial force and the bending moment in columns is directly taken into account, and the deterioration in the cyclic behavior of these members is implicitly considered. The superiority of the calibrated FB-FLPH modelling approach is examined compared with the cases in which conventional fi ber-based distributed plasticity and concentrated plasticity models are utilized. The effi ciency of the enumerated modelling techniques is probed when they are implemented to model the columns of a typical special moment frame in order to prove the advantage of the FB-FLPH modelling approach.

Kinematics modeling of a 6-PSS parallel mechanism with wide-range flexure hinges

A novel 6-PSS flexible parallel mechanism was presented,which employed wide-range flexure hinges as passive joints.The proposed mechanism features micron level positioning accuracy over cubic centimeter scale workspace.A three-layer back-propagation(BP) neural network was utilized to the kinematics analysis,in which learning samples containing 1 280 groups of data based on stiffness-matrix method were used to train the BP model.The kinematics performance was accurately calculated by using the constructed BP model with 19 hidden nodes.Compared with the stiffness model,the simulation and numerical results validate that BP model can achieve millisecond level computation time and micron level calculation accuracy.The concept and approach outlined can be extended to a variety of applications.

Seismic Response and Stability Analysis of Single Hinged Articulated Tower

Study of dynamic stability phenomenon in transient systems has always created interest amongst the researchers because of its inherent non-linearities. Offshore structures subjected to wave, earthquake or wind loads or a combination of these loads show non-linear transient behaviour. As oceanic waves are better modelled as stochastic process, there is a need to investigate the stochastic stability of flexible offshore structures as well. Present study has been carried out to determine seismic response of Single Hinged Articulated Tower (SHAT) under different categories of wave loads and earthquake followed by its dynamic stability analysis. Different phases of wave/earthquake loading on SHAT have been explored to investigate dynamic instabilities existing during each phase. Two dimensional phase plots have been used to identify phases of dynamic instability existing within the responses of SHAT under various conditions of loading.

Optimization of Bottom-hinged Flap-type Wave Energy Converter for a Specific Wave Rose

In this paper, we conducted a numerical analysis on the bottom-hinged flap-type Wave Energy Convertor (WEC). The basic model, implemented through the study using ANSYS-AQWA, has been validated by a three-dimensional physical model of a pitching vertical cylinder. Then, a systematic parametric assessment has been performed on stiffness, damping, and WEC direction against an incoming wave rose, resulting in an optimized flap-type WEC for a specific spot in the Persian Gulf. Here, stiffness is tuned to have a near-resonance condition considering the wave rose, while damping is modified to capture the highest energy for each device direction. Moreover, such sets of specifications have been checked at different directions to present the best combination of stiffness, damping, and device heading. It has been shown that for a real condition, including different wave heights, periods, and directions, it is very important to implement the methodology introduced here to guarantee device performance.