A new digital Gaussian pulse shaping algorithm based on bilinear transformation

Nuclear pulse signal needs to be transformed to a suitable pulse shape to remove noise and improve energy resolution of a nuclear spectrometry system. In this paper, a new digital Gaussian shaping method is proposed.According to Sallen-Key analog Gaussian shaping filter circuits, the system function of Sallen-Key analog Gaussian shaping filter is deduced on the basis of Kirchhoff laws. The system function of the digital Gaussian shaping filter based on bilinear transformation is deduced too. The expression of unit impulse response of the digital Gaussian shaping filter is obtained by inverse z-transform. The response of digital Gaussian shaping filter is deduced from convolution sum of the unit impulse response and the digital nuclear pulse signal. The simulation and experimental results show that the digital nuclear pulse has been transformed to a pulse with a pseudo-Gaussian, which confirms the feasibility of the new digital Gaussian pulse shaping algorithm based on bilinear transformation.

Nonlocal symmetries and negative hierarchies related to bilinear Bcklund transformation

In this paper, nonlocal symmetries defined by bilinear Baacklund transformation for bilinear potential Kd V（p Kd V）equation are obtained. By introducing an auxiliary variable which just satisfies the Schwartzian form of Kd V（SKd V）equation, the nonlocal symmetry is localized and the Levi transformation is presented. Besides, based on three different types of nonlocal symmetries for potential Kd V equation, three sets of negative p Kd V hierarchies along with their bilinear forms are constructed. An impressive result is that the coefficients of the third type of（bilinear） negative p Kd V hierarchy（N 〉 0） are variable, which are obtained via introducing an arbitrary parameter by considering the translation invariance of the p Kd V equation.

In the Atmosphere and Oceanic Fluids:Scaling Transformations,Bilinear Forms,Bäcklund Transformations and Solitons for A Generalized Variable-Coefficient Korteweg-de Vries-Modified Korteweg-de Vries Equation

The atmosphere is an evolutionary agent essential to the shaping of a planet,while in oceanic science and daily life,liquids are commonly seen.In this paper,we investigate a generalized variable-coefficient Korteweg-de Vriesmodified Korteweg-de Vries equation for the atmosphere,oceanic fluids and plasmas.With symbolic computation,beginning with a presumption,we work out certain scaling transformations,bilinear forms through the binary Bell polynomials and our scaling transformations,N solitons(with N being a positive integer)via the aforementioned bilinear forms and bilinear auto-Bäcklund transformations through the Hirota method with some solitons.In addition,Painlevé-type auto-Bäcklund transformations with some solitons are symbolically computed out.Respective dependences and constraints on the variable/constant coefficients are discussed,while those coefficients correspond to the quadratic-nonlinear,cubic-nonlinear,dispersive,dissipative and line-damping effects in the atmosphere,oceanic fluids and plasmas.

Soliton Solutions and Bilinear Bcklund Transformation for Generalized Nonlinear Schrdinger Equation with Radial Symmetry

Investigated in this paper is the generalized nonlinear Schrdinger equation with radial symmetry.Withthe help of symbolic computation, the one-, two-, and N-soliton solutions are obtained through the bilinear method.Bcklund transformation in the bilinear form is presented, through which a new solution is constructed.Graphically, wehave found that the solitons are symmetric about x=0, while the soliton pulse width and amplitude will change alongwith the distance and time during the propagation.

Bcklund Transformation and Multisoliton Solutions in Terms of Wronskian Determinant for (2+1)-Dimensional Breaking Soliton Equations with Symbolic Computation

In this paper, two types of the (2+1)-dimensional breaking soliton equations are investigated, whichdescribe the interactions of the Riemann waves with the long waves.With symbolic computation, the Hirota bilinearforms and Bcklund transformations are derived for those two systems.Furthermore, multisoliton solutions in termsof the Wronskian determinant are constructed, which are verified through the direct substitution of the solutions intothe bilinear equations.Via the Wronskian technique, it is proved that the Bcklund transformations obtained are theones between the (N-1)-and N-soliton solutions.Propagations and interactions of the kink-/bell-shaped solitonsare presented.It is shown that the Riemann waves possess the solitonic properties, and maintain the amplitudes andvelocities in the collisions only with some phase shifts.

Casoratian Solutions to Toda Lattice Via Its Backlund Transformation

Generalized Casoratian condition and Casoratian solutions of the Toda lattice are given in terms of its bilinear Backlund transformation. By choosing suitable Casoratian entries and parameter in the bilinear Backlund transformation, we can give transformations among many kinds of solutions.

Generalized Wronskian Solutions to Modified Korteweg-de Vries Equation via Its Bcklund Transformation

In the paper we discuss the Wronskian solutions of modified Korteweg-de Vries equation (mKdV) via theBcklund transformation (BT) and a generalized Wronskian condition is given,which allows us to substitute an arbitrarycoefficient matrix in the G_N(t) for the original diagonal one.

改进的基于PSE和Tustin变换的分数阶系统求解递推算法

以分数阶算子近似方法的分析研究为基础,基于Tustin变换理论及其用于分数阶算子的离散生成函数公式特点,利用二项式幂函数的Maclaurin展开能够保证收敛的特性,考虑常用算法的局限性,提出了一种改进的基于幂级数展开和Tustin变换的分数阶运算方法,并应用于线性分数阶系统的求解,给出了递推算法的详细推导。算例仿真及其分析表明,该算法有效且具有良好的运算速度和精度。

(3+1)维广义非线性发展方程的双线性Backlund变换与精确解

基于Hirota双线性方法和试探函数法,研究一个(3+1)维广义非线性发展方程的双线性Backlund变换和精确解问题。用Hirota双线性法,构造(3+1)维广义非线性发展方程的双线性形式和双线性Backlund变换。基于双线性形式和双线性Backlund变换,利用试探函数法与符号计算系统Mathematica,获得(3+1)维广义非线性发展方程的多种精确解,包括呼吸波解、复合型解、Lump周期解和孤子解,并分析解的相互作用情况。

(1+1)维的具有时间与空间色散的五阶方程

研究了一个新的(1+1)维的具有时空色散可积五阶方程,推广了方程的形式,并探讨了色散关系及其各自的系数情况.利用简化Hirota方法推导了方程的可积条件,导出了多孤子解.此外,利用指数型初始解构造方程的变换,得出双线性方程,继而利用Hirota双线性导数法导出单孤子解、双孤子解及N孤子解.结合双线性方程给出了不同双线性交换算子的双线性Bäcklund变换,继而导出不同条件下的双曲行波解、周期行波解等行波解.

Painlevé analysis, auto-Bäcklund transformations, bilinear forms and soliton solutions for a(2+1)-dimensional variable-coefficient modified dispersive water-wave system in fluid mechanics

In this paper,we investigate a(2+1)-dimensional variable-coefficient modified dispersive waterwave system in fluid mechanics.We prove the Painlevéintegrability for that system via the Painlevéanalysis.We find some auto-B?cklund transformations for that system via the truncated Painlevéexpansions.Bilinear forms and N-soliton solutions are constructed,where N is a positive integer.We discuss the inelastic interactions,elastic interactions and soliton resonances for the two solitons.We also graphically demonstrate that the velocities of the solitons are affected by the variable coefficient of that system.

Hilbert spectrum and intrinsic oscillation mode of dynamic response of a bilinear SDOF system: influence of harmonic excitation amplitude

Under harmonic wave excitation, the dynamic response of a bilinear SDOF system can be expressed by the Hilbert spectrum. The Hilbert spectrum can be formulated by (1) the inter-wave combination mechanism between the steady response and the transient response when the system behaves linearly, or (2) the intra-wave modulation mechanism embedded in one intrinsic mode function (IMF) component when the system behaves nonlinearly. The temporal variation of the instantaneous frequency of the IMF component is consistent with the system nonlinear behavior of yielding and unloading. As a thorough study of this fundamental structural dynamics problem, this article investigates the influence of the amplitude of the harmonic wave excitation on the Hilbert spectrum and the intrinsic oscillatory mode of the dynamic response of a bilinear SDOF system.

基于Hirota方法探求非零边界条件下MNLS/DNLS方程的孤子解

Hirota双线性导数变换处理非线性偏微分方程,是一种比反散射变换更为方便的直接方法。本文展示了Hirota双线性导数变换法应用于求解非线性可积方程的一般手续,以非零驻波边界条件下修正的非线性薛定谔(MNLS)方程为例,探求其孤子解;再通过简单的参数归零法直接得到导数非线性薛定谔(DNLS)方程在非零常数边界条件下的相应孤子解,亮/暗孤子解随时间和空间变量的演化也通过图像加以演示,所得孤子解与反散射方法得到的结果一致相符。

一类(1+1)维变系数复方程的可积性研究

该文基于双Bell多项式与Hirota双线性算子之间的关系,研究了一类(1+1)维变系数复方程的可积性.首先通过适当的变换,构造出方程的双线性表达式、双线性Backlund变换,又通过Hopf-Cole变换得到方程的Lax对,从而证明该方程具有Lax可积性.

基于深度双线性转换注意力机制网络的林业有害生物识别方法

【目的】针对林业有害生物种类多,不少物种之间相似度高,视觉差异小,不易区分,导致林业防控人员无法快速准确识别有害生物种类的问题,本文提出基于深度双线性转换注意力机制网络(DBTANet)的林业有害生物细粒度图像识别方法。【方法】以自然状态下拍摄的60种林业害虫和14种林业有害植物图像作为研究对象,利用水平镜像、亮度调节、高斯模糊和高斯噪声等方法对图像数据集进行增强,按6∶2∶2比例划分为训练集、验证集和测试集;采用双线性插值法将每幅图像缩放至统一尺寸;改进ResNet网络中残差模块,加入深度双线性转换模块和注意力机制模块,建立DBTANet-101网络进行特征提取与分类;利用平均准确率、平均召回率和平均F1值3个指标评价不同模型对林业有害生物的识别结果。【结果】VGGNet-19、ResNet-50、ResNet-101、改进残差模块的ResNet-50和ResNet-101共5个模型对74种林业有害生物平均准确率分别为78.6%、74.9%、76.3%、79.7%和81.1%;在改进残差模块的ResNet-101基础上,增加深度双线性转换模块和注意力机制模块后,74种林业有害生物的平均准确率和召回率分别提高了10.2%和12.1%,22种相似的有害生物细粒度图像平均准确率提高了15.7%。【结论】基于深度双线性转换注意力机制网络(DBTANet)的林业有害生物细粒度图像识别方法,对74种林业有害生物和22种相似有害生物细粒度图像的平均准确率分别为91.3%和85.1%;双线性转换模块和注意力机制可以有效提高林业有害生物识别模型的准确率。

用Hirota双线性导数变换求MNLS方程的Rogue波解

修正的非线性薛定谔方程(MNLS方程)与导数非线性薛定谔方程(DNLS方程)是两个紧密相关且完全可积的非线性偏微分方程.该文通过Hirota双线性导数变换方法,首先求得MNLS方程在平面简谐波背景下的空间周期解,即Akhmediev型呼吸子解,再通过长波极限得其Rogue波解.根据简单的参数归零法使之自然地约化为DNLS方程的Rogue波解,并借助于一个积分变换将其变换为Chen-Lee-Liu方程的Rogue波解.文章还简要讨论了MNLS方程和DNLS方程在非局域情形整体解的存在性问题.

基于离散域改进PIR控制的PMSM电流谐波抑制策略

在表贴式永磁同步电机(PMSM)矢量控制系统中,固定的比例积分谐振(PIR)控制器参数会在运行工况变化时导致电流谐波抑制效果变差,为此,提出一种改进的离散域控制器参数设计方法。首先,通过频率特性曲线对比加入谐振控制器后电流环幅频响应,分析连续域谐振参数整定方法的局限性。其次,推导离散域谐振数字控制器表达式,并给出离散域电流环稳定性证明过程。最后,以调制比为约束条件,构建满足系统稳定的离线谐振增益切换表。为解决谐振增益稳定切换的问题,采用滞环控制算法实现谐振增益在不同转速区间的平滑切换。最终,通过仿真和实验结果可知,基于离线切换表的改进比例积分谐振控制器在不同转速工况时,既满足了系统的稳定性,又实现了抑制5、7次电流谐波的效果。

基于拉普拉斯变换构建校正窄频速度记录的传递函数

受窄频地震仪平坦响应范围影响,窄频速度记录存在低频成分失真问题,导致地震记录可用范围受限。针对此问题,本文推导基于拉普拉斯变换和双线性变换的传递函数,实现由窄频地震记录向宽频地震记录的校正,并以日本Hi-net速度记录为例进行验证,将校正后的速度记录与同台KiK-net加速度积分所得的速度记录予以对比。结果显示,原始速度记录在低频处存在失真,而校正后的波形与KiK-net加速度积分速度记录波形一致,这表明改进的传递函数能有效地解决原速度记录中的低频成分失真问题,有效地拓宽了低频可使用范围,而且相较于Nakata校正速度记录方法,以本文给出的传递函数校正的速度记录在振幅和波形等方面的精度更高。

改进型永磁同步电机有限控制集模型预测速度控制

永磁同步电机传统有限集模型预测速度控制策略中电压矢量方向固定,可选矢量范围具有一定局限性,输出电压的突然变化,会导致电流纹波较大。因此,提出了一种基于电压细分的有限控制集模型预测控制(FCS-MPC)直接速度控制策略。所提策略在FCS-MPC方案中引入了一组具有可调振幅和可移动原点特征的有限电压细分矢量作为候选电压,同时为了获得更准确的电流预测,使用了双线性变换(即Tustin变换)积分近似。该控制器能够预测未来电流和速度,并使用脉宽调制输出最佳细分电压。采用两电平三相逆变器驱动的永磁同步电机进行仿真验证结果表明,与传统的FCS-MPC方案相比,所提策略有效地减小了电流纹波,拓宽了电压矢量选择的范围,同时提高了电机鲁棒性。

基于多粒度特征融合的叶片分类与分级方法

长期以来,已有很多工作致力于研究植物叶片分类,虽然它们在公开数据集上表现较好,但实际应用并不理想,且难以应用于更复杂的问题,如叶片分级,即要求在对叶片进行分类的基础上,再对同一类的叶片进行更细级别(质量等级)的划分。为此,提出了一种新的植物叶片分类以及分级模型,该模型关注叶片的多粒度信息,并将粗粒度与细粒度进行有效融合。该模型包含粗粒度和细粒度两个分支,由粒度混合损失将两个分支联系起来,促使模型逐步学习由粗到细的粒度表征。采用了多步骤训练方式,每一步提取不同层级的特征,实现浅层特征与深层特征的融合。此外,还提出了几何通道注意力模块,该模块由空间变换和双线性注意力池化组成,使模型可以关注图像中更具区分度的局部区域,提取出的特征更具区分性。所提方法在Flavia leaf和Swedish leaf两个公开的叶片分类数据集上分别达到了99.8%和99.7%的分类准确率,且在所构建的烟叶分级数据集上达到了71.9%的分级准确率,均超过了目前最优的方法。