STOCHASTIC OPTIMAL CONTROL OF STRONGLY NONLINEAR SYSTEMS UNDER WIDE-BAND RANDOM EXCITATION WITH ACTUATOR SATURATION

A bounded optimal control strategy for strongly non-linear systems under non-white wide-band random excitation with actuator saturation is proposed. First, the stochastic averaging method is introduced for controlled strongly non-linear systems under wide-band random excitation using generalized harmonic functions. Then, the dynamical programming equation for the saturated control problem is formulated from the partially averaged Itō equation based on the dynamical programming principle. The optimal control consisting of the unbounded optimal control and the bounded bang-bang control is determined by solving the dynamical programming equation. Finally, the response of the optimally controlled system is predicted by solving the reduced Fokker-Planck-Kolmogorov （FPK） equation associated with the completed averaged Itō equation. An example is given to illustrate the proposed control strategy. Numerical results show that the proposed control strategy has high control effectiveness and efficiency and the chattering is reduced significantly comparing with the bang-bang control strategy.

Optimal control strategies for stochastically excited quasi partially integrable Hamiltonian systems

In this paper two different control strategies designed to alleviate the response of quasi partially integrable Hamiltonian systems subjected to stochastic excitation are proposed. First, by using the stochastic averaging method for quasi partially integrable Hamiltonian systems, an n-DOF controlled quasi partially integrable Hamiltonian system with stochastic excitation is converted into a set of partially averaged It^↑o stochastic differential equations. Then, the dynamical programming equation associated with the partially averaged It^↑o equations is formulated by applying the stochastic dynamical programming principle. In the first control strategy, the optimal control law is derived from the dynamical programming equation and the control constraints without solving the dynamical programming equation. In the second control strategy, the optimal control law is obtained by solving the dynamical programming equation. Finally, both the responses of controlled and uncontrolled systems are predicted through solving the Fokker-Plank-Kolmogorov equation associated with fully averaged It^↑o equations. An example is worked out to illustrate the application and effectiveness of the two proposed control strategies.

Modal parameter identification of flexible spacecraft using the covariance-driven stochastic subspace identification(SSI-COV) method

In this paper, the on-orbit identification of modal parameters for a spacecraft is investigated. Firstly, the coupled dynamic equation of the system is established with the Lagrange method and the stochastic state-space model of the system is obtained. Then, the covariance-driven stochastic subspace identification（SSI-COV） algorithm is adopted to identify the modal parameters of the system. In this algorithm, it just needs the covariance of output data of the system under ambient excitation to construct a Toeplitz matrix, thus the system matrices are obtained by the singular value decomposition on the Toeplitz matrix and the modal parameters of the system can be found from the system matrices. Finally,numerical simulations are carried out to demonstrate the validity of the SSI-COV algorithm. Simulation results indicate that the SSI-COV algorithm is effective in identifying the modal parameters of the spacecraft only using the output data of the system under ambient excitation.

Time-delayed feedback control optimization for quasi linear systems under random excitations

A strategy for time-delayed feedback control optimization of quasi linear systems with random excitation is proposed. First, the stochastic averaging method is used to reduce the dimension of the state space and to derive the stationary response of the system. Secondly, the control law is assumed to be velocity feedback control with time delay and the unknown control gains are determined by the performance indices. The response of the controlled system is predicted through solving the Fokker-Plank-Kolmogorov equation associated with the averaged Ito equation. Finally, numerical examples are used to illustrate the proposed control method, and the numerical results are confirmed by Monte Carlo simulation .

A kind of noise-induced transition to noisy chaos in stochastically perturbed dynamical system

We investigate a kind of noise-induced transition to noisy chaos in dynamical systems. Due to similar phenomenological structures of stable hyperbolic attractors excited by various physical realizations from a given stationary random process, a specific Poincar6 map is established for stochastically perturbed quasi-Hamiltonian system. Based on this kind of map, various point sets in the Poincar6＇s cross-section and dynamical transitions can be analyzed. Results from the customary Duffing oscillator show that, the point sets in the Poincare＇s global cross-section will be highly compressed in one direction, and extend slowly along the deterministic period-doubling bifurcation trail in another direction when the strength of the harmonic excitation is fixed while the strength of the stochastic excitation is slowly increased. This kind of transition is called the noise-induced point-overspreading route to noisy chaos.

Monitoring the Modal Frequency and Velocity Variations of Bridges under Ambient Excitation

We conducted a long-term monitoring experiment on the Lutuanxilu Bridge located in Changping District of Beijing, employing our recently developed real-time bridge monitoring system based on the Guralp CMG-6TD broadband seismometer. We identified the modal parameters with the stochastic subspace identification( SSI) algorithm,and continuously monitored the temporal velocity variation with coda wave interferometry.The results show that:( 1) the highly sensitive Guralp CMG-6TD broadband seismometer,which records the three-component vibration signal within broad frequency range,is well suited for long-term bridge health monitoring.( 2) With the continuous vibration signal from ambient excitation,the stochastic subspace algorithm can robustly identify the low-order modal parameters and the coda wave interferometry can accurately monitor the tiny velocity variation.( 3) The elastic modulus of bridge materials changes significantly associated with varying temperature,leading to diurnal velocity variation with amplitude of approximately 1%. The velocity variation shows strong negative correlation with temperature fluctuation. Meanwhile,the modal frequencies remain quite stable,suggesting that the velocity variation may be a more sensitive quantitative damage index.( 4) While the modal frequencies reflect the integrated health status of the bridge,the velocity variation can be utilized to monitor the local elastic modulus. Therefore,it is crucial for bridge health monitoring to continuously monitor the two key damage indexes under ambient excitation.

The Hierarchical Stochastic Schrodinger Equations: Theory and Applications

The hierarchical stochastic Schrodinger equations(HSSE)are a kind of numerically exact wavefunction-based approaches suitable for the quantum dynamics simulations in a relatively large system coupled to a bosonic bath.Starting from the influence-functional description of open quantum systems,this review outlines the general theoretical framework of HSSEs and their concrete forms in different situations.The applicability and efficiency of HSSEs are exemplified by the simulations of ultrafast excitation energy transfer processes in large-scale systems.

Importance Sampling Strategy for Oscillatory Stochastic Processes

This paper contributes to the structural reliability problem by presenting a novel approach that enables for identification of stochastic oscillatory processes as a critical input for given mechanical models. Identification development follows a transparent image processing paradigm completely independent of state-of-the-art structural dynamics, aiming at delivering a simple and wide purpose method. Validation of the proposed importance sampling strategy is based on multi-scale clusters of realizations of digitally generated non-stationary stochastic processes. Good agreement with the reference pure Monte Carlo results indicates a significant potential in reducing the computational task of first passage probabilities estimation, an important feature in the field of e.g., probabilistic seismic design or risk assessment generally.

Radio Interference Characteristic of Ultra-high Voltage AC Transmission Lines by Using Stochastic Modeling

For developing ultra-high voltage(UHV) AC power transmission systems,it is important to precisely estimate and to limit the radio interference(RI) level of power lines.Based on the stochastic characteristics in amplitude and repetition rate of induced corona current,by using the probability theory and mathematical statistics,we establish a stochastic model for the wide-sense stationary random process of corona discharges.Then combining the stochastic model with model-propagation-analysis method,the RI levels under three-phase UHV AC transmission lines are calculated.The results of the calculation based on stochastic model method and International Council on Large Electric Systems(CIGRE) excitation function are compared with that based on semi-empirical method and some other excitation functions.The stochastic model based on different excitation functions is also adopted to simulate the RI levels under finite test lines with two opened terminations.The results indicate that with the same average maximum gradient on conductor surface and the same conductor type,the number of corona discharge per unit length is one of the main reasons that causes the difference between different excitation functions.It is also concluded that for a long test line,the effect of standing wave on RI field strength is negligible in the middle of the line,but obvious near both terminations: for a 10-km line,the maximum difference in RI field strength is 2.78 dB,between the peak value of the standing wave near the ends and the steady value near the middle of the line.

The CDF and its sensitivity analysis of stochastic structure with stochastic excitation by advanced stratified line sampling

For the stochastic structure with stochastic excitation, an advanced stratified line sampling (SLS) method is presented to obtain the cumulative distribution function (CDF) of the structural response and its sensitivity. The advanced stratified line sampling method introduces a set of middle failure subsets firstly. And for each subset, the conventional line sampling can be used to obtain the corresponding value of the response's CDF. At the same time, the sensitivity estimations of each failure subset can also be computed by modifying the important direction and corresponding reliability coefficients. The properties of CDF sensitivity are proved while the performance function is linear with normal random variables. After two simple examples are used to demonstrate the properties of CDF sensitivity and the feasibility of the presented method, the method employed to analyze the CDF and corresponding sensitivity of root bending moment (RBM) responses for the stochastic BAH is wing with gust excitation to a square-edged gust and to a Dryden gust. The results show that the parameters of the second and the fifth order modals exert more influence on the CDF of response than the other ones, and the presented SLS method can more significantly reduce the computational cost compared with Monte Carlo simulation (MCS).

ON THE TWO BIFURCATIONS OF A WHITE-NOISE EXCITED HOPF BIFURCATION SYSTEM

The present work is concerned with the behavior of the second bifurcation of a Hopf bifurcation system excited by white-noise. It is found that the intervention of noises induces a drift of the bifurcation point along with the subtantial change in bifurcation type.

Equivalent Stochastic Linearization for Nonlinear Uncertain Structure Under Stationary Gaussian Stochastic Excitation

Equivalent stochastic linearization （ESL） for nonlinear uncertain structure under stationary stochastic excitation is presented. There are two parts of difference between the original system and equivalent system： one is caused by the difference between the means of original and equivalent stochastic structure; and another is caused by the difference between the original and equivalent stochastic structure which has the relation with stochastic variables. Statistical characteristics of equivalent stochastic structure can be obtained in accordance with mean square criterion, so nonlinear stochastic structure is transformed into linear stochastic structure. In order to attain that objective, the compound response spectrum of linear stochastic structure under stationary random excitation which is used in the solution is derived in the case of the mutual independence between stochastic excitation and stochastic structure. Finally, the example shows the accuracy and validity of the proposed method.

基于虚拟激励法的磁浮车桥耦合系统随机振动分析

为探讨随机轨道不平顺作用下中低速磁浮列车和桥梁的动力响应,将虚拟激励法引入磁浮车桥振动分析中,提出中低速磁浮车辆-悬浮控制系统-桥梁耦合系统随机振动分析方法.将中低速磁浮列车简化为弹簧阻尼器连接的多刚体,悬浮系统中电流使用比例-微分(PD)控制方法进行主动控制,采用有限元方法对桥梁进行建模,将随机轨道不平顺转换为一系列简谐波构成的虚拟激励;编制中低速磁浮车桥动力系统随机振动分析程序,自动生成系统随机振动方程,利用分离迭代方法对磁浮车辆控制方程和桥梁动力方程进行求解计算.研究结果表明:虚拟激励法能够高效计算中低速磁浮车桥系统随机动力响应,其计算效率约为蒙特卡洛方法的1/11,基于虚拟激励法能够获得中低速磁浮车桥动力系统均值、标准差和时变功率谱密度等统计结果.

非平稳随机激励下高维非线性系统可靠度分析的概率密度全局演化方法

实际工程结构遭受的灾害性动力作用(如强风、地震等)往往具有显著的随机性和非平稳性。对复杂随机激励下高维非线性系统的动力可靠度进行精细化分析,对于实际工程结构的抗灾设计和优化具有重要意义。基于一般连续随机过程的降维概率密度演化方程,给出了一类非平稳随机激励下的高维非线性系统动力可靠度分析方法。具体地,若仅针对系统某一感兴趣物理量在给定安全域下的首次超越问题,则可以构造该物理量在安全域内的吸收边界过程,并建立其瞬时概率密度函数满足的二维偏微分方程,即降维概率密度演化方程。方程中的本征漂移系数是驱动概率密度演化的全局性物理驱动力,可以通过对原系统有限次代表性确定性动力分析获取的数据进行数值构造。采用数值方法求解降维概率密度演化方程,即可获得系统的动力可靠度解答。文中通过两个算例验证了该方法的有效性,并讨论了需要进一步研究的问题。

Stability and performance analysis of the compressed Kalman filter algorithm for sparse stochastic systems

This paper considers the problem of estimating unknown sparse time-varying signals for stochastic dynamic systems.To deal with the challenges of extensive sparsity,we resort to the compressed sensing method and propose a compressed Kalman filter(KF)algorithm.Our algorithm first compresses the original high-dimensional sparse regression vector via the sensing matrix and then obtains a KF estimate in the compressed low-dimensional space.Subsequently,the original high-dimensional sparse signals can be well recovered by a reconstruction technique.To ensure stability and establish upper bounds on the estimation errors,we introduce a compressed excitation condition without imposing independence or stationarity on the system signal,and therefore suitable for feedback systems.We further present the performance of the compressed KF algorithm.Specifically,we show that the mean square compressed tracking error matrix can be approximately calculated by a linear deterministic difference matrix equation,which can be readily evaluated,analyzed,and optimized.Finally,a numerical example demonstrates that our algorithm outperforms the standard uncompressed KF algorithm and other compressed algorithms for estimating high-dimensional sparse signals.

半主动调谐质量阻尼器对随机人群荷载振动控制

为提高人行桥的舒适度,提出了一种可变质量与阻尼的半主动调谐质量阻尼器(STMD)。该STMD不但能通过水泵和电磁阀等驱动装置实时调节质量以重调频率来适应人行桥动力特性的变化,而且能实时改变电涡流阻尼的磁导间距来调节阻尼系数以提高耗能效果。首先介绍了STMD变质量及变阻尼的算法及模型试验,然后进行基于人群激励概率性随机模型的案例分析。对比研究了无控结构、优化设计的被动TMD、变质量STMD、变阻尼STMD及变质量变阻尼STMD在随机协同人群荷载下的100次加速度响应,通过这100组加速度的最大值、均方根(RMS)值及最大1-s RMS值共3个舒适度评估指标的最大值、平均值和标准差,分析了不同TMD的减振效果及鲁棒性。研究结果表明,由于人群荷载和人体参数的随机性,结构的动力响应有较大的差异。整体而言,可同时变质量变阻尼的STMD具有最佳的减振效果,且其标准差也最小,即具有最好的鲁棒性。

Response regimes of narrow-band stochastic excited linear oscillator coupled to nonlinear energy sink

This paper draws attention to the issue of the vibration absorption of nonlinear mechani- cal system coupled to nonlinear energy sink （NES） under the impact of the narrow band stochastic excitation. Firstly, based on the complex-averaging method and frequency detuning methodology, response regimes of oscillators have been researched under the linear impact of coupling a nonlinear attachment with less relativistic mass and an external sinusoidal forcing, of which results turn out that the quasi-periodicity response regime of system which occurs when the external excitation amplitude exceeds the critical values will be the precondition of the targeted energy transfer. Secondly, basing on the path integration method, vibration suppression of NES has been researched when it is affected by a main oscillator with a narrow band stochastic force in the form of trigono- metric functions, of which results show that response regimes are affected by the amplitude of stochastic excitation and the disturbance strength. Finally, all these conclusions have been approved by the numerical verification and coincided with the theoretical analysis; meanwhile, after the com- paring analysis with the optimal linear absorber, it turns out that the NES which is affected by the narrow band stochastic force could also suppress the vibration of system with a better effect.

强噪声与非周期脉冲激励下单稳系统的随机共振及应用

随机共振是噪声背景下非线性系统对微弱特征信号的最优响应,能够对微弱特征信号进行增强。偏置单稳态系统相较于传统的双稳态系统,对非周期脉冲激励具有良好的共振特性。然而,非线性系统的参数影响系统的最优输出,对不同的非周期脉冲激励,系统难以自适应调节。针对上述问题,该研究强噪声与非周期脉冲激励下偏置单稳态自适应随机共振。首先,基于优化算法实现不同非周期脉冲激励下的自适应随机共振。然后,以强噪声背景下钢丝绳漏磁检测信号为应用对象,经偏置单稳态系统自适应随机共振输出后,以峰峰值作为损伤特征演化评价指标,评估不同微弱损伤特征间的差异。同时,应用偏置单稳态自适应随机共振法和自适应移位平均法对强噪声背景下钢丝绳漏磁信号进行对比分析,以峰峰值增益和信噪比增益为指标,结果表明偏置单稳态自适应随机共振法效果优于自适应移位平均法。最后,讨论了噪声强度对单稳态自适应随机共振的影响,发现偏置单稳态自适应随机共振具有较强的抗噪能力。

随机激励作用下船舶横摇运动的奇异非混沌动力学

基于一类规则横浪作用下的单自由度船舶横摇运动模型,考虑恢复力矩和阻尼力矩的非线性因素,以一低干舷船模为例,利用龙格库塔法求解了横摇运动方程,通过时间庞加莱截面绘制了系统的分岔图;考虑其受随机风荷载扰动下不同周期吸引子演变成奇异非混沌吸引子的具体过程,发现周期激励系统在随机激励扰动下同样存在奇异非混沌吸引子,且当分岔参数离混沌区域越远,所需要随机激励的幅值越大才能诱发奇异非混沌吸引子.通过最大李雅普诺夫指数验证吸引子的非混沌性;采用奇异连续谱和分形图刻画吸引子的奇异性.

Response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control

We studied the response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control using the stochastic averaging method. First, the time-delayed feedback bang-bang control force is expressed approximately in terms of the system state variables without time delay. Then the averaged It6 stochastic differential equations for the system are derived using the stochastic averaging method. Finally, the response of the system is obtained by solving the Fokker-Plank-Kolmogorov （FPK） equation associated with the averaged lt6 equations. A Duffing oscillator with time-delayed feedback bang-bang control under combined harmonic and white noise excitations is taken as an example to illus- trate the proposed method. The analytical results are confirmed by digital simulation. We found that the time delay in feedback bang-bang control will deteriorate the control effectiveness and cause bifurcation of stochastic jump of Duffing oscillator.