The Convergence of the Steepest Descent Algorithm for D.C.Optimization

Some properties of a class of quasi-differentiable functions（the difference of two finite convex functions） are considered in this paper. And the convergence of the steepest descent algorithm for unconstrained and constrained quasi-differentiable programming is proved.

An Enhanced Steepest Descent Method for Global Optimization-Based Mesh Smoothing

In order to speed up the global optimization-based mesh smoothing, an enhanced steepest descent method is presented in the paper. Numerical experiment results show that the method performs better than the steepest descent method in the global smoothing. We also presented a physically-based interpretation to explain why the method works better than the steepest descent method.

A NEW STEPSIZE FOR THE STEEPEST DESCENT METHOD

The steepest descent method is the simplest gradient method for optimization. It is well known that exact line searches along each steepest descent direction may converge very slowly. An important result was given by Barzilar and Borwein, which is proved to be superlinearly convergent for convex quadratic in two dimensional space, and performs quite well for high dimensional problems. The BB method is not monotone, thus it is not easy to be generalized for general nonlinear functions unless certain non-monotone techniques being applied. Therefore, it is very desirable to find stepsize formulae which enable fast convergence and possess the monotone property. Such a stepsize αk for the steepest descent method is suggested in this paper. An algorithm with this new stepsize in even iterations and exact line search in odd iterations is proposed. Numerical results are presented, which confirm that the new method can find the exact solution within 3 iteration for two dimensional problems. The new method is very efficient for small scale problems. A modified version of the new method is also presented, where the new technique for selecting the stepsize is used after every two exact line searches. The modified algorithm is comparable to the Barzilar-Borwein method for large scale problems and better for small scale problems.

Fractional-order global optimal backpropagation machine trained by an improved fractional-order steepest descent method

We introduce the fractional-order global optimal backpropagation machine,which is trained by an improved fractionalorder steepest descent method(FSDM).This is a fractional-order backpropagation neural network(FBPNN),a state-of-the-art fractional-order branch of the family of backpropagation neural networks(BPNNs),different from the majority of the previous classic first-order BPNNs which are trained by the traditional first-order steepest descent method.The reverse incremental search of the proposed FBPNN is in the negative directions of the approximate fractional-order partial derivatives of the square error.First,the theoretical concept of an FBPNN trained by an improved FSDM is described mathematically.Then,the mathematical proof of fractional-order global optimal convergence,an assumption of the structure,and fractional-order multi-scale global optimization of the FBPNN are analyzed in detail.Finally,we perform three(types of)experiments to compare the performances of an FBPNN and a classic first-order BPNN,i.e.,example function approximation,fractional-order multi-scale global optimization,and comparison of global search and error fitting abilities with real data.The higher optimal search ability of an FBPNN to determine the global optimal solution is the major advantage that makes the FBPNN superior to a classic first-order BPNN.

CONVERGENCE ANALYSIS OF A LOCALLY ACCELERATED PRECONDITIONED STEEPEST DESCENT METHOD FOR HERMITIAN-DEFINITE GENERALIZED EIGENVALUE PROBLEMS

By extending the classical analysis techniques due to Samokish, Faddeev and Faddee- va, and Longsine and McCormick among others, we prove the convergence of the precon- ditioned steepest descent with implicit deflation （PSD-id） method for solving Hermitian- definite generalized eigenvalue problems. Furthermore, we derive a nonasymptotie estimate of the rate of convergence of the PSD-id method. We show that with a proper choice of the shift, the indefinite shift-and-invert preconditioner is a locally accelerated preconditioner, and is asymptotically optimal which leads to superlinear convergence Numerical examples are presented to verify the theoretical results on the convergence behavior of the PSD- id method for solving ill-conditioned Hermitian-definite generalized eigenvalue problems arising from electronic structure calculations. While rigorous and full-scale convergence proofs of preconditioned block steepest descent methods in practical use still largely eludes us, we believe the theoretical results presented in this paper shed light on an improved understanding of the convergence behavior of these block methods.

A multipath mitigation algorithm for GNSS signals based on the steepest descent approach

Multipath interference seriously degrades the performance of Global Navigation Satellite System(GNSS)positioning in an urban canyon.Most current multipath mitigation algorithms suffer from heavy computational load or need external assistance.We propose a multipath mitigation algorithm based on the steepest descent approach,which has the merits of less computational load and no need for external aid.A new ranging code tracking loop is designed based on the steepest descent method,which can save an early branch or a late branch compared with the narrow-spacing correlation method.The power of the Non-Line-of-Sight(NLOS)signal is weaker than that of the Line-of-Sight(LOS)signal when the LOS signal is not obstructed and with a relatively high Carrier Noise Ratio(CNR).The peak position in the X-axis of the ranging code autocorrelation function does not move with the NLOS interference.Meanwhile,the cost function is designed according to this phenomenon.The results demonstrate that the proposed algorithm outperforms the narrow-spacing correlation and the Multipath Estimated Delay Locked Loop(MEDLL)in terms of the code multipath mitigation and computation time.The Standard Deviation(STD)of the tracking error with the proposed algorithm is less than 0.016 chips.Moreover,the computation time of the proposed algorithm in a software defined receiver is shortened by 24.21%compared with the narrow-spacing correlation.

Thrust Optimization of Flapping Wing via Gradient Descent Technologies

The current work aims at employing a gradient descent algorithm for optimizing the thrust of a flapping wing. An in-house solver has been employed, along with mesh movement methodologies to capture the dynamics of flow around the airfoil. An efficient framework for implementing the coupled solver and optimization in a multicore environment has been implemented for the generation of optimized solutionsmaximizing thrust performance & computational speed.

Three-step relaxed hybrid steepest-descent methods for variational inequalities

The classical variational inequality problem with a Lipschitzian and strongly monotone operator on a nonempty closed convex subset in a real Hilbert space is studied. A new three-step relaxed hybrid steepest-descent method for this class of variational inequalities is introduced. Strong convergence of this method is established under suitable assumptions imposed on the algorithm parameters.

针对频率失调问题的挖掘机ANC系统优化设计

在进行窄带主动噪声控制(Narrowband Active Noise Control,NANC)过程中,常采用非声学传感器来获取参考信号,但非声学传感器会因老化和疲劳积累产生误差,使NANC系统频率失调(Frequency Mismatch,FM),导致降噪性能下降,甚至失效。针对此问题,提出一种基于自适应补偿(Adaptive Compensation,AC)的控制方案,该方案利用滤波增强信号与原始信号的相关性,设计一个频率跟踪质量评价因子,使该方案能更精准地实现对频率的追踪,以取得更优的FM补偿效果。通过仿真对比发现,与传统解决方案相比,AC方案能应对更大FM,使NANC系统具有更好的稳定性,初步验证了算法的优越性。进一步开展台架试验与实机实验,试验结果表明:当FM达到10%,经AC方案优化的NANC系统对挖掘机2、4、6阶噪声降噪量仍达到了15.2 dB、24.1 dB、21.2 dB,进一步验证了AC方案的性能。同时,也表明所提AC方案能有效实现对FM的控制,具有较高的实用价值。

Interseismic slip distribution and locking characteristics of the mid-southern segment of the Tanlu fault zone

We employ the block negative dislocation model to invert the distribution of fault coupling and slip rate deficit on the different segments of the Tanlu(Tancheng-Lujiang) fault zone, according to the GPS horizontal velocity field from 1991 to 2007(the first phase) and 2013 to 2018(the second phase). By comparing the deformation characteristics results, we discuss the relationship between the deformation characteristics with the M earthquake in Japan. The results showed that the fault coupling rate of the northern section of Tancheng in the second phase reduced compared with that in the first phase. However, the results of the two phases showed that the northern section of Juxian still has a high coupling rate, a deep blocking depth, and a dextral compressive deficit, which is the enrapture section of the 1668 Tancheng earthquake. At the same time, the area strain results show that the strain rate of the central and eastern regions of the second phase is obviously enhanced compared with that of the first phase. The occurrence of the great earthquake in Japan has played a specific role in alleviating the strain accumulation in the middle and south sections of the Tanlu fault zone. The results of the maximum shear strain show that the shear strain in the middle section of the Tanlu fault zone in the second phase is weaker than that in the first phase, and the maximum shear strain in the southern section is stronger than that in the first phase. The fault coupling coefficient of the south Sihong to Jiashan section is high, and it is also the unruptured section of historical earthquakes. At the same time, small earthquakes in this area are not active and accumulate stress easily, so the future earthquake risk deserves attention.

基于变增益最速梯度下降法的表贴式永磁同步电机位置修正策略

滑模观测器具有响应速度快、鲁棒性强等优点,已广泛应用于表贴式永磁同步电机无位置传感器的中、高速控制系统。然而,具有固定参数的滑模观测器很难在宽速度范围内保持一致的估算精度,而采用基于速度观测器带宽限制的方法进行噪声和扰动抑制会降低电机的动态性能。针对上述问题,该文首先分析滑模观测器估算表贴式永磁同步电机转子位置的误差产生机理,提出一种新型位置误差观测器,主要思想是基于磁链观测进行位置误差连续估算,并采用最速梯度下降法对积分过程进行反馈校正;然后,通过变增益循环迭代优化提高位置误差观测器的速度与准确性;最后搭建表贴式永磁同步电机加载测试平台进行实验,结果验证了所提方法具有位置观测精度高、鲁棒性强的特点。

基于非负约束的重力向下延拓BTTB-MRNSD方法

向下延拓作为处理与解释重力数据的一项重要技术,因其计算的不适定性而备受研究人员的关注。空间域延拓方法一般延拓精度较高,但通常计算复杂度较大。本文首先根据重力异常数据的特点,借鉴图像复原问题的处理思路,提出了一种重力向下延拓等效数学模型。然后,基于系数矩阵的块-托普利茨-托普利茨-块(BTTB)结构特点,本文提出了一种具有非负约束的空间-波数混合域下延迭代方法。该方法克服了空间域延拓计算复杂度大的问题,计算效率较高。基于理论重力模型和实测异常数据的对比试验表明,本文提出的重力下延方法具有相对较高的下延精度和稳定性,且收敛性较好。

双三相永磁同步电机鲁棒滑模预测速度控制

为提高双三相永磁同步电机系统应对复杂扰动时的鲁棒性,提出了一种带有最速下降观测器的滑模预测速度控制策略。通过将参数变化和外部扰动注入到q轴电流系数,建立了带有扰动的双三相永磁同步电机运动模型。基于电机扰动模型提出了一种滑模预测速度控制策略,该方案使用基于双曲正切函数的新型幂次趋近律,能够在保持较快跟踪速度的同时有效抑制滑模抖振。设计了一个基于最速下降算法的扰动观测器,用于估计随叠加扰动而时刻变化的q轴电流系数并将其传递到滑模预测速度控制模型中。与传统的滑模预测速度控制相比,仿真结果证明了所提方法具有较好的动态跟踪性能和扰动抑制性能。

航空装备缓冲气囊设计与缓冲特性研究

航空装备缓冲气囊以重量小、成本低等优势成为航空装备缓冲系统的研究热点。为快速解决航空装备缓冲气囊的设计问题,本文运用数值仿真软件,以航空装备缓冲气囊为研究对象,依据运动学、工程热力学及柔性薄壳力学等理论建立了环形缓冲气囊的数值仿真模型,利用最速下降法对模型进行优化设计;将优化参数的仿真结果与试验结果进行对比,验证模型建立的正确性,并分析不同参数(开口面积、开口压力和气囊高度)对缓冲气囊缓冲特性的影响。结果表明,当其他参数一定时,随着开口面积增加,缓冲过载减小,着地速度增加;随着开口压力增加,缓冲过载增加,着地速度减小;随着气囊高度增加,缓冲过载减小,着地速度变化不大。本文仿真方法可以迅速确定缓冲气囊的关键设计参数(如开口面积、排气压力、缓冲高度等)与外形,可以提升缓冲气囊的设计效率,为研究气囊缓冲特性提供了理论依据。

改进的高阶收敛FastICA算法

高阶收敛的FastICA具有形式简单、收敛速度快的特点,但其对初始值的选择比较敏感,若初始值选择不当很容易影响收敛的效果,甚至造成不收敛的结果.针对这一问题,采用最速下降法对三阶和五阶收敛的FastICA算法进行改进.首先,应用最速下降法求出初值,再用高阶收敛的FastICA算法求出最优解.语音信号的分离实验表明:改进后的算法对混合信号进行了较好的分离,并且有效地克服了初值敏感性的问题.

大功率GTO等效传热模型的研究

研究发现ＧＴＯ 动态热阻变化率的对数具有分区间近似线性的规律，提出可采用分段拟合的方法初步获得ＧＴＯ的高阶传热模型。基于最速下降原理构造了一种迭代算法，可以精确整定等效传热模型的各个参数，并研究了下降因子对迭代收敛性的影响。与ＧＴＯ 的实测动态热阻曲线比较，该模型的计算误差在±３％ 以内。将此传热模型集成在损耗分析软件中，可分析ＧＴＯ的瞬态传热特性。

用于JPEG图像的高容量信息隐藏算法

使用JPEG图像的DCT系数作为隐藏载体,通过一种改进的量化嵌入算法提高了信息隐藏的容量.算法以基于结构相似度的图像质量指标作为图像的失真度量,以最速下降法选择嵌入算法中的控制参数,保证了数据嵌入后的图像具有较低的失真水平.实验结果表明本文提出的算法提高了信息隐藏的容量,并较好地平衡了失真和容量之间的关系.

几种优化方法在频率域全波形反演中的应用效果及对比分析研究

全波形反演方法是一个有效求解参数重建问题的方法,其本质是一个寻找最优解的优化问题,目前多用局部最优方法求解,如最速下降法、共轭梯度法、高斯-牛顿法、拟牛顿法等.文中给出了常用的优化方法,基于二维声波方程,将这些方法应用于部分overthrust模型的反演,通过对各方法所得反演模型的精度和计算时间的对比分析,对各个方法的优缺点进行总结,为后续多参数反演或高维方程参数反演提供方法选择上的参考;针对所要求解的反问题,选用的优化方法需要在收敛速率、计算存储量和算法的稳定性之间进行权衡,以得到一个最优的反演结果.

层状介质中重力、地震联合反演的迭代算法

本文提出一种用于层状介质中重力、地震资料联合反演层速度、层密度及弯曲界面深度的迭代算法。该方法通过引入加权最小平方目标泛函,将层状介质中的重力、地震资料联合反演问题转化成具体的优化问题。为了得到反问题的最优解,文中系统地研究了层状介质中双摄动处理技术,以及层状介质中波场摄动的一阶 Born 近似解与理论重力异常摄动解。并应用 Tarantola 的反演理论,导出了梯度算子的计算公式。然后应用最速下降法给出了求取最优解的具体算法,得到了一种类似于地震偏移与空间更投影的迭代反演方法。对理论模型进行重力、地震联合反演的结果表明,该方法不仅可碱少未知参数的个数,提高反演的收敛速度,而且可减少反演的不适定性,不失为一种可行的多参数反演方法。