光纤陀螺反馈回路非线性的影响与对策

在设计闭环光纤陀螺的过程中发现,数模转换器D/A以及Y波导等器件的非线性容易导致陀螺出现死区及标度因数误差。为此,从理论上分析了光纤陀螺反馈回路的非线性误差对光纤陀螺性能的影响。通过分析可知,当Sagnac相移小于反馈回路积分非线性误差引起的相位差,并且反馈回路的差分非线性误差较大时,则容易引起阶梯波不能正常复位导致死区,也分析了反馈回路非线性误差对陀螺标度因数误差的影响,并进行了仿真及实验。为了防止反馈回路非线性误差引起的死区问题,提出了一种在反馈信号中叠加均值为零的方波信号方法,并通过后续信号处理中的平均过程消除了反馈回路非线性误差影响。     

单片集成MEMS陀螺数字闭环接口ASIC电路设计

为提高MEMS陀螺的线性度和稳定性,设计了适用于电容式MEMS陀螺的数字式双闭环接口电路。首先,概括了接口电路的系统结构,包括电容/电压转换电路、高精度模数转换器、数字信号处理等模块。然后,设计了基于自动增益控制的陀螺驱动闭环控制系统,并分析了驱动闭环稳定性条件,为驱动闭环系统的快速调试提供理论指导。最后,提出了一种基于四阶机电结合∑△调制器原理的陀螺敏感闭环检测系统。接口电路在0.18μm高压CMOS工艺平台上完成流片,并且与MEMS陀螺结构封装在一个管壳中进行测试验证。测试结果表明本接口电路的优越性能:在±500°/s量程下陀螺非线性度达到52.8 ppm,陀螺零偏不稳定性为0.58°/h(Allan方差),角度随机游走等于0.07°/h~(1/2),满足高性能MEMS陀螺对高线性度、高稳定性接口电路的应用需求。     

数字闭环光纤陀螺死区机理分析

结合工程实际，对基于集成光学多功能芯片的数字闭环光纤陀螺中的死区机理进行理论分析，并进行了实验验证。相位调制器的模拟驱动电压信号在数字反馈阶梯波复位作用下能产生不同的工作模式，探测器的输出微弱信号因此受到幅值和相位均不同的电子串扰。以方波调制和四态波调制为例，研究了光纤陀螺中电子串扰的作用方式、电子串扰的转换方式和形成死区的过程等问题。在上述基础上，根据需要设计了专门的可编程的光纤陀螺高速数据采集电路，对死区机理进行了研究试验。最后还从优化陀螺电路印制板设计和优化信号调制解调算法等方面进行阐述，以解决数字闭环光纤陀螺死区问题。     

基于Faraday效应的光纤陀螺频率特性评估方法

由于角振动台的振动频率有限,无法实现光纤陀螺的高带宽测试。提出了基于Faraday效应的光纤陀螺频率特性评估方法,采用正弦电流激励下的Faraday相位差等效Sagnac相位差,解决了激励信号输出频率有限的问题。根据光纤中的Faraday效应原理,分析了该评估方法与光纤陀螺角振动台测试方法的等效性;搭建了评估系统,使用该评估系统来模拟某型号光纤陀螺的信号处理过程,进行等效评估实验,得到了等效评估的光纤陀螺闭环带宽为9 kHz,实现了高带宽光纤陀螺的频率特性评估测试,为改善光纤陀螺的动态特性提供了有效的验证平台。     

基于粒子滤波的光纤陀螺寻北方案

为了降低噪声对光纤陀螺（FOG）寻北的影响,提高寻北速度和精度,提出了一种基于粒子滤波（PF）的光纤陀螺寻北方案。首先基于单轴光纤陀螺能够敏感地球自转角速率水平分量的输出特性,建立非线性光纤陀螺寻北系统的状态空间模型和观测模型。根据粒子滤波的基本原理,以及在解决非线性系统估计问题上的优势,利用粒子滤波来解算出光纤陀螺敏感轴与真北方向的夹角。仿真实验结果表明,该方案不仅可以在20至30倍采样时间间隔内快速获得寻北结果,而且可以有效解决光纤陀螺常值漂移和随机噪声的影响,其精度优于基于扩展卡尔曼滤波（EKF）的寻北结果。     

基于高斯粒子滤波的陀螺ARIMA模型辨识方法

ARIMA模型是陀螺信号处理中的一种重要方法,研究ARIMA模型辨识方法对提高陀螺精度有着重要意义。针对常规ARIMA建模滤波方法应用于光纤陀螺时滤波精度较低的问题,在ARMA模型基础上建立了一种适用于中低精度光纤陀螺的非平稳随机过程的ARIMA模型,提出了基于高斯粒子滤波的光纤陀螺ARIMA模型辨识方法。将光纤陀螺的ARIMA模型辨识与状态估计相结合,构建非线性的滤波模型,利用光纤陀螺实测信号进行了实验,结果表明所提出的方法能够有效地抑制光纤陀螺随机噪声,具有较高的工程应用价值。     

数字闭环光纤陀螺频率特性分析与测试

系统的闭环带宽严重影响光纤陀螺在振动、急转弯等环境条件下的测试精度,闭环光纤陀螺的实际带宽高达几kHz,无法采用一般的角振动台进行全频带频率特性测试,因此,频率特性的分析与测试成为了闭环光纤陀螺研究的一项重要内容。针对这种需求,根据系统的结构框图及工作原理,建立了数字闭环光纤陀螺的动态模型,推导出了系统的传递函数;在此基础上对数字闭环光纤陀螺的频率特性进行了分析,指出了改善系统动态特性的方法;最后,利用数字闭环光纤陀螺的闭环工作原理,通过在反馈阶梯波上直接叠加激励信号,实现了光纤陀螺阶跃响应和频率响应的测试,得出了系统闭环带宽高达9kHz的结论。     

随机噪声作用下梁结构的非线性振动研究

考虑随机噪声影响,研究一端固支一端夹支的梁结构在横向外激励扰动下的非线性振动。首先,基于里兹-伽辽金法得到梁的振动控制方程并将其无量纲化,随后引入随机噪声进一步得到系统的随机动力学模型。在此基础上考虑高斯白噪声和有界噪声,分别研究2种随机噪声对梁结构随机动力学行为的影响,并利用随机Melnikov法求出系统的混沌阈值,得到2种随机噪声影响下系统的三维混沌阈值图。由数值计算结果可知,阻尼系数、外激励幅值和随机噪声对梁结构的振动都有影响,且阻尼小、外激励幅值大和随机噪声强都更容易导致随机系统产生混沌运动。此外,通过本研究可以分析比较不同随机噪声(如高斯白噪声和有界噪声)对梁结构振动状态的影响,从而以抑制梁结构在随机噪声影响下产生混沌运动为目的,提出更好的降噪方法。     

基于增益自补偿的光纤陀螺瞬态噪声抑制方法

在光纤陀螺稳定控制平台应用领域中,光纤陀螺相位滞后及瞬态噪声严重制约着随动控制系统的控制品质。为了提高基于光纤陀螺随动系统的控制效果,研究了基于增益自补偿的光纤陀螺瞬态噪声抑制方法。首先,分析了由于死区补偿带来的光纤陀螺瞬态噪声,在此基础上研究了基于增益自补偿的光纤陀螺瞬态噪声抑制方法,并对该方法进行了理论分析。根据稳定控制平台对相位滞后和瞬态噪声的设定要求,通过一只数字闭环光纤陀螺进行了测试验证,测试结果满足系统对相位滞后和瞬态噪声的指标要求,瞬态噪声峰峰值为0.36(°)/s,并不随增益的变化而变化,验证了增益自补偿方法的有效性。     

光纤陀螺基于本征模态函数筛选的阈值滤波算法

为降低光纤陀螺随机噪声,提高其测量精度,利用周期图法辨识光纤陀螺的随机噪声特征参数,针对其噪声特征,提出了基于本征模态函数筛选的微分经验模态分解阈值滤波算法。以本征模态函数和原始信号二者的概率密度函数的空间距离为判别依据,对所有本征模态函数进行筛选,根据已估计的噪声参数计算阈值大小,采用时间序列阈值的方法对筛选出的本征模态函数进行处理。仿真和实验结果表明,该滤波算法能够在跟踪光纤陀螺信号变化的同时,使其零偏不稳定性下降90.35%,角随机游走下降93.75%,对随机噪声有较好的抑制能力。     

Modeling of stochastic modulated rattling system

Rattling vibration is an important noise source of gear-box. To control that noise, it is necessary to elaborate a mathematics-mechanical model on rattling gears. In this paper, a rattling system modulated by noise was investigated. Instead of performing the very tedious numerical calculation, a discrete stochastic model described by three dimensional mean mapping was established by means of the Non-Gaussian closure technique. Through the example, the chaotic stochastic behavior may be revealed. In comparison with deterministic model, the model developed in this paper is more approximate to practice and more available for acoustic investigation, so that it is suggested to be applied to modeling on rattling vibration.     

Stochastic Traveling Wave Solution to a Stochastic KPP Equation

In this paper, we consider the stochastic KPP equation which is perturbed by an environmental noise. Applying an extended stochastic ordering technique, we establish the existence of a stochastic traveling wave solution to the equation and give a sufficient condition under which solutions can be attracted to the stochastic traveling wave.     

Stochastic bifurcation in duffing system subject to harmonic excitation and in presence of random noise

A global analysis of stochastic bifurcation in a special kind of Duffing system, named as Ueda system, subject to a harmonic excitation and in presence of random noise disturbance is studied in detail by the generalized cell mapping method using digraph. It is found that for this dissipative system there exists a steady state random cell flow restricted within a pipe-like manifold, the section of which forms one or two stable sets on the Poincare cell map. These stable sets are called stochastic attractors (stochastic nodes), each of which owns its attractive basin. Attractive basins are separated by a stochastic boundary, on which a stochastic saddle is located. Hence, in topological sense stochastic bifurcation can be defined as a sudden change in character of a stochastic attractor when the bifurcation parameter of the system passes through a critical value. Through numerical simulations the evolution of the Poincare cell maps of the random flow against the variation of noise intensity is explored systematically. Our study reveals that as a powerful tool for global analysis, the generalized cell mapping method using digraph is applicable not only to deterministic bifurcation, but also to stochastic bifurcation as well. By this global analysis the mechanism of development, occurrence, and evolution of stochastic bifurcation can be explored clearly and vividly.     

Dynamical responses of airfoil models with harmonic excitation under uncertain disturbance

In this paper, we investigate nonlinear dynamical responses of two-degree-of-freedom airfoil (TDOFA) models driven by harmonic excitation under uncertain disturbance. Firstly, based on the deterministic airfoil models under the harmonic excitation, we introduce stochastic TDOFA models with the uncertain disturbance as Gaussian white noise. Subsequently, we consider the amplitude–frequency characteristic of deterministic airfoil models by the averaging method, and also the stochastic averaging method is applied to obtain the mean-square response of given stochastic TDOFA systems analytically. Then, we carry out numerical simulations to verify the effectiveness of the obtained analytic solution and the influence of harmonic force on the system response is studied. Finally, stochastic jump and bifurcation can be found through the random responses of system, and probability density function and time history diagrams can be obtained via Monte Carlo simulations directly to observe the stochastic jump and bifurcation. The results show that noise can induce the occurrence of stochastic jump and bifurcation, which will have a significant impact on the safety of aircraft.     

高斯色噪声和谐波激励共同作用下耦合SD振子的混沌研究

耦合SD振子作为一种典型的负刚度振子, 在工程设计中有广泛应用. 同时高斯色噪声广泛存在于外界环境中, 并可能诱发系统产生复杂的非线性动力学行为, 因此其随机动力学是非线性动力学研究的热点和难点问题. 本文研究了高斯色噪声和谐波激励共同作用下双稳态耦合SD振子的混沌动力学, 由于耦合SD振子的刚度项为超越函数形式, 无法直接给出系统同宿轨道的解析表达式, 给混沌阈值的分析造成了很大的困难. 为此, 本文首先采用分段线性近似拟合该振子的刚度项, 发展了高斯色噪声和谐波激励共同作用下的非光滑系统的随机梅尔尼科夫方法. 其次, 基于随机梅尔尼科夫过程, 利用均方准则和相流函数理论分别得到了弱噪声和强噪声情况下该振子混沌阈值的解析表达式, 讨论了噪声强度对混沌动力学的影响. 研究结果表明, 随着噪声强度的增大混沌区域增大, 即增大噪声强度更容易诱发耦合SD振子产生混沌. 当阻尼一定时, 弱噪声情况下混沌阈值随噪声强度的增加而减小; 但是强噪声情况下噪声强度对混沌阈值的影响正好相反. 最后, 数值结果表明, 利用文中的方法研究高斯色噪声和谐波激励共同作用下耦合SD振子的混沌是有效的.本文的结果为随机非光滑系统的混沌动力学研究提供了一定的理论指导.      

Direct Derivation of Corrective Terms in SDE Through Nonlinear Transformation on Fokker–Planck Equation

This paper examines the problem of probabilistic characterization of nonlinear systems driven by normal and Poissonian white noise. By means of classical nonlinear transformation the stochastic differential equation driven by external input is transformed into a parametric-type stochastic differential equation. Such equations are commonly handled with Itô-type stochastic differential equations and Itô's rule is used to find the response statistics. Here a different approach is proposed, which mainly consists in transforming the Fokker–Planck equation for the original system driven by external input, in the transformed probability density function of the new state variable. It will be shown that the Wong–Zakay or Stratonovich corrective term and the hierarchy of correction terms in the case of Poissonian white noise arise in a natural way.     

Trichotomous noise induced stochastic resonance in a linear system

We investigate stochastic resonance in an underdamped linear system subjected to multiplicative trichotomous noise. We carry out the Shapiro?CLoginov formula to find the exact expression of output amplitude gain, and the impacts of the input signal frequency and noise parameters will be observed, such as noise switching rate or noise correlation time, noise amplitude and noise flatness. Then one can find the stochastic resonance for the proposed linear system.     

随机振动控制系统中含未知噪声方差的自适应滤波

通过构造出关于模型噪声和量测噪声的方差的泛函,以泛函数极小为目标,提出了随机振动控制系统中含未知噪声方差的自适应滤波优化准则,用ＤＦＰ优化方法求解出模型噪声和量测噪声的方差,从而保证Ｋａｌｍａｎ滤波的结果为最优,并应用ＬＱＧ方法实现振动控制。     

Dissipative Stochastic Evolution Equations Driven by General Gaussian and Non-Gaussian Noise

We study a class of stochastic evolution equations with a dissipative forcing nonlinearity and additive noise. The noise is assumed to satisfy rather general assumptions about the form of the covariance function; our framework covers examples of Gaussian processes, like fractional and bifractional Brownian motion and also non Gaussian examples like the Hermite process. We give an application of our results to the study of the stochastic version of a common model of potential spread in a dendritic tree. Our investigation is specially motivated by possibility to introduce long-range dependence in time of the stochastic perturbation.