A nonlinear dynamics method for signal identification

When a radio frequency signal is radiated by a transmitter, the properties of the transmitter itself affect the properties of the signal. These transmitter-induced changes are known as unintentional modulation, to differentiate them from intentional modulation used to add information to the signal. The unintentional modulation can be used to identify which transmitter produced a signal. This paper shows how phase space analysis based on nonlinear dynamics ideas can be used to determine which of several amplifiers produced a signal.     

Optical efficiency of solar concentrators by a reverse optical path method

A method for the optical characterization of a solar concentrator, based on the reverse illumination by a Lambertian source and measurement of intensity of light projected on a far screen, has been developed. It is shown that the projected light intensity is simply correlated to the angle-resolved efficiency of a concentrator, conventionally obtained by a direct illumination procedure. The method has been applied by simulating simple reflective nonimaging and Fresnel lens concentrators.     

电动舵机非线性系统的辨识研究

本文针对所设计的三闭环电动舵机系统,为了提高舵机的控制精度,提出了采用非线性系统辨识的方法,并且利用辨识的参数对系统进行补偿。根据电动舵机的模型分别采用了前馈补偿的方法和反馈辨识的方法对系统的摩擦进行仿真建模研究,并且将建模数据加入到电动舵机中进行试验验证,系统的位置跟踪误差和速度跟踪误差均有大幅度减小。试验结果证明,本文所提出的辨识研究方法可以准确地实现摩擦模型的建立,并且从该模型出发进行补偿可以有效地提高电动舵机的控制精度。     

A nonlinear signal-based control method and its applications to input identification for nonlinear SIMO problems

The problem of control system design can be conceptualised as identifying an input signal to a plant (the system to be controlled) so that the corresponding output matches that of a pre-defined reference signal. Primarily, this problem is solved via well-known techniques based upon the principle of feedback design, an essential component for ensuring stability and robustness of the controlled system. However, feedforward design techniques also have a large part to play, whereby (in the absence of feedback control and assuming that the plant is stable) a model of the plant dynamics can be used to modify the reference signal so that the resultant feedforward input signal generates a plant output signal that is sufficiently close to the original reference signal.     

随机参激和外激联合作用下非线性动力系统的路径积分解

将基于Gauss Legendre公式的路径积分法推广到随机参激和外激联合作用的非线性动力系统.研究了受高斯白噪声参激和外激联合作用的非线性振子，将所得路径积分解与其精确解（满足一定条件时该系统存在精确解）或Monte Carlo随机模拟结果相比较，充分验证了路径积分的准确性.并借助路径积分数值解，捕捉到该随机系统的一维P分岔. 关键词： 路径积分 P分岔 随机参激 随机外激     

反卷积波束形成识别电机冷却系噪声辐射路径

为更准确地识别某电机冷却系噪声的辐射路径,基于FFT-NNLS反卷积波束形成方法对其进行试验研究。结果表明:相比于传统波束形成,FFT-NNLS反卷积波束形成能够显著提高分辨率,更准确地识别声源;224 Hz风扇叶片通过频率和400~1200 Hz频段的噪声水平较高,分别占声源计算面总噪声的17.7%和49.1%;冷却液入口是最主要的噪声辐射路径、进气口次之、出气口相对较弱。     

Nonparametric identification of nonlinear dynamic systems using a synchronisation-based method

The present study proposes an identification method for highly nonlinear mechanical systems that does not require a priori knowledge of the underlying nonlinearities to reconstruct arbitrary restoring force surfaces between degrees of freedom. This approach is based on the master–slave synchronisation between a dynamic model of the system as the slave and the real system as the master using measurements of the latter. As the model synchronises to the measurements, it becomes an observer of the real system. The optimal observer algorithm in a least-squares sense is given by the Kalman filter. Using the well-known state augmentation technique, the Kalman filter can be turned into a dual state and parameter estimator to identify parameters of a priori characterised nonlinearities. The paper proposes an extension of this technique towards nonparametric identification. A general system model is introduced by describing the restoring forces as bilateral spring-dampers with time-variant coefficients, which are estimated as augmented states. The estimation procedure is followed by an a posteriori statistical analysis to reconstruct noise-free restoring force characteristics using the estimated states and their estimated variances. Observability is provided using only one measured mechanical quantity per degree of freedom, which makes this approach less demanding in the number of necessary measurement signals compared with truly nonparametric solutions, which typically require displacement, velocity and acceleration signals. Additionally, due to the statistical rigour of the procedure, it successfully addresses signals corrupted by significant measurement noise. In the present paper, the method is described in detail, which is followed by numerical examples of one degree of freedom (1DoF) and 2DoF mechanical systems with strong nonlinearities of vibro-impact type to demonstrate the effectiveness of the proposed technique.     

On the problem of nonlinear distortions of the maximum-entropy method

We consider the problem of nonlinear distortions resulting from noise in the input data in the reconstruction of images from incomplete Fourier spectra using nonlinear information-theoretic methods, in particular, the maximum-entropy method. Comparison of traditional and generalized maximum-entropy methods shows that generalized methods, which operate in the space of complex functions, provide the best agreement of the solution with the data and, therefore, a minimal level of nonlinear distortions. Recommendations for processing of real nonnegative images of incoherent radio sources are given.Institute of Applied Astronomy, Russian Academy of Sciencies St. Petersburg. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, No. 12, pp. 1267–1277, December, 1995.     

Stochastic collocation method for secondary bifurcation of a nonlinear aeroelastic system

A stochastic collocation method is proposed to investigate the secondary bifurcation of a two-dimensional aeroelastic system with structural nonlinearity represented by cubic restoring forces, and uncertainties expressed by random parameters in the cubic stiffness coefficient and in the initial pitch angle. The accuracy of the stochastic collocation method is improved by incorporating higher order schemes, such as piecewise cubic interpolation and piecewise cubic spline interpolation, instead of a piecewise linear interpolation formula. For an aeroelastic problem with the uncertainty expressed by a time dependent combination of five random variables, an efficient collocation method is developed using a sparse grid approach with a dimension adaptive strategy. Numerical simulations are carried out to demonstrate the effectiveness of the proposed method for long term computation and discontinuous problems.     

圆形阵列光电探测系统双目标识别方法

针对双弹丸同时着靶情况下的立靶坐标测量问题,提出一种圆形阵列光电探测系统的双目标识别方法.采用光电探测器件组成1个圆形的探测阵列,并将3个发光角度均为60°的扇形一字线激光器均匀设置于圆形探测阵列上组成探测光幕.当2发弹丸同时穿过探测光幕时,会在圆形探测阵列上产生6个弹丸投影,通过信号处理电路识别6个弹丸投影的中心位置...     

Lagrangian of the most probable path for one dimensional nonlinear diffusion processes

Using a Lagrangian density of the Fokker-Planck equation and the Kolmogoroff backward equation we construct a Lagrangian of the most probable path for one dimensional nonlinear diffusion processes.     

An improved method for Darboux transformation for the coupled inhomogeneous nonlinear Schrödinger system from plasma physics and nonlinear optics

The coupled inhomogeneous nonlinear Schrödinger-type system which can be used to control soliton propagation and interaction in certain plasmas and optical fibers is investigated. An improved method for Darboux transformation (DT) is presented in more general forms by constructing an improved Γ$\Gamma$-Riccati-type Bäcklund transformation (Γ$\Gamma$-R BT). With the N$N$th-iterated Γ$\Gamma$-R BT or the N$N$th-iterated DT, which is a compact representation for the N$N$-soliton-like solutions and can generate a series of analytic solutions from a pair of the seed solutions through algebraic manipulations, the analytic one-/two-soliton-like solutions are provided. With the choice of parameters for the soliton solutions, the dynamical characteristics of the influences of the inhomogeneous parameters on the propagation of the soliton pulses are discussed graphically.     

无焦压缩光路系统的计算机辅助装调方法

为了解决随机成分多、调节灵敏度高的离轴反射式系统的精确装调问题,介绍了干涉测量与计算机优化技术相结合的方法,建立了各元件失调量与初级像差之间的关系,以及元件间的像差相互补偿关系,通过干涉测量采集系统全视场的波前差,反向优化得到各元件的失调量,在波长为632.8 nm时,无焦压缩光路系统全视场平均出射波前优于RMS0.055 ,压缩比误差小于5,实现了无焦压缩光路系统高精度、高效率的装调。     

An iterative method for nonlinear dynamical system of an electrostatically actuated micro-cantilever

This study proposes an iterative method, in which all iterations are linear, for solving the nonlinear dynamical system of an electrostatically actuated micro-cantilever in MEMS. The presented method is further improved, so that the CPU time needed is significantly reduced. This method provides solutions in excellent agreement with numerical ones.     

On the spectrum of the system of interacting quantum nonlinear resonances

Correlation functions of the density matrix components and the frequency spectrum are numerically analysed in the system of two interacting quantum nonlinear resonances. For overlapping resonances and a sufficiently large number of resonance-trapped levels the motion of the system is shown to be close to stochasticity.     

A path integral method for data assimilation

Described here is a path integral, sampling-based approach for data assimilation, of sequential data and evolutionary models. Since it makes no assumptions on linearity in the dynamics, or on Gaussianity in the statistics, it permits consideration of very general estimation problems. The method can be used for such tasks as computing a smoother solution, parameter estimation, and data/model initialization.Speedup in the Monte Carlo sampling process is essential if the path integral method has any chance of being a viable estimator on moderately large problems. Here a variety of strategies are proposed and compared for their relative ability to improve the sampling efficiency of the resulting estimator. Provided as well are details useful for its implementation and testing.The method is applied to a problem in which standard methods are known to fail, an idealized flow/drifter problem, which has been used as a testbed for assimilation strategies involving Lagrangian data. It is in this kind of context that the method may prove to be a useful assimilation tool in oceanic studies.