基于state-space-split法的滞回非线性系统随机动力响应分析

采用SSS(state-space-split)法,建立了引入Bouc-Wen滞回模型的杜芬非线性系统在高斯白噪声激励下的概率密度函数(PDF)的近似求解方法,分析了其随机动力响应变化规律。首先,将Bouc-Wen滞回模型引入杜芬非线性系统,分别考虑非线性系统中的几何非线性和材料非线性对动力响应的影响。随后,对该模型进行了等效线性化(EQL)处理,基于等效线性化法结果,介绍了SSS法的简化方法和计算原理,并通过该方法求解了三维FPK方程的近似联合概率密度函数。最后,将该方法应用于三个案例和一个工程实例,通过求解其概率密度函数分布及动力可靠度验证了提出方法的适用性、可行性和优越性。

An Improved Time Domain Approach for Analysis of Floating Bridges Based on Dynamic Finite Element Method and State-Space Model

The floating bridge bears the dead weight and live load with buoyancy,and has wide application prospect in deep-water transportation infrastructure.The structural analysis of floating bridge is challenging due to the complicated fluid-solid coupling effects of wind and wave.In this research,a novel time domain approach combining dynamic finite element method and state-space model(SSM)is established for the refined analysis of floating bridges.The dynamic coupled effects induced by wave excitation load,radiation load and buffeting load are carefully simulated.High-precision fitted SSMs for pontoons are established to enhance the calculation efficiency of hydrodynamic radiation forces in time domain.The dispersion relation is also introduced in the analysis model to appropriately consider the phase differences of wave loads on pontoons.The proposed approach is then employed to simulate the dynamic responses of a scaled floating bridge model which has been tested under real wind and wave loads in laboratory.The numerical results are found to agree well with the test data regarding the structural responses of floating bridge under the considered environmental conditions.The proposed time domain approach is considered to be accurate and effective in simulating the structural behaviors of floating bridge under typical environmental conditions.

Least Squares Matrix Algorithm for State-Space Modelling of Dynamic Systems

This work presents a novel least squares matrix algorithm (LSM) for the analysis of rapidly changing systems using state-space modelling. The LSM algorithm is based on the Hankel structured data matrix representation. The state transition matrix is updated without the use of any forgetting function. This yields a robust estimation of model parameters in the presence of noise. The computational complexity of the LSM algorithm is comparable to the speed of the conventional recursive least squares (RLS) algorithm. The knowledge of the state transition matrix enables feasible numerical operators such as interpolation, fractional differentiation and integration. The usefulness of the LSM algorithm was proved in the analysis of the neuroelectric signal waveforms.

A Study on the Factors Influencing the Income Gap between Urban and Rural Areas Based on State-space Model

The increasingly widening income gap between urban and rural areas is affected by many factors. Using the stepwise regression analysis,we find that urbanization level,socio-economic development,education level,financial development scale and financial development efficiency have the greatest impact on the income gap between urban and rural areas. By cointegration test,it is found that there is a long-term equilibrium relationship between these five variables and the income gap between urban and rural areas. We build the state-space model to research the dynamic impact of these factors on the income gap between urban and rural areas. The results show that by improving the level of urbanization,we can effectively narrow the income gap between urban and rural areas,while socio-economic development,the improvement of education level,expansion of financial development scale and financial development efficiency all significantly expand the income gap between urban and rural areas.

Discrete Simulation of Flexible Plate Structure Using State-Space Formulation

This paper presents the development of dynamic simulation of a flexible plate structure with various boundary conditions. A flexible square plate is considered. A finite-difference method is used to discretise the governing partial differential equation formulation describing its dynamic behaviour. The model thus developed has been validated against characteristic parameters of the plate. The model thus developed is further formulated using discrete state-space representation, to allow easy and fast implementation for simulating the dynamic behaviour of the plate with various boundary conditions. The simulation algorithm thus developed is validated, and accurate results with representation of the first five modes of vibration of the plate have been achieved. The algorithm thus developed is used in subsequent research work as a platform for development and verification of suitable control strategies for vibration suppression of flexible plate structures.

Improved State-space Modelling for Microgrids Without Virtual Resistances

Power converters and their interfacing networks are often treated as modular state-space blocks for small-signal stability studies in microgrids;they are interconnected by matching the input and output states of the network and converters.Virtual resistors have been widely used in existing models to generate a voltage for state-space models of the network that require voltage inputs.This paper accurately quantifies the adverse impacts of adding the virtual resistance and proposes an alternative method for network modelling that eliminates the requirement of the virtual resistor when interfacing converters with microgrids.The proposed nonlinear method allows initialization,time-domain simulations of the nonlinear model,and linearization and eigenvalue generation.A numerically linearized small-signal model is used to generate eigenvalues and is compared with the eigenvalues generated using the existing modelling method with virtual resistances.Deficiencies of the existing method and improvements offered by the proposed modelling method are clearly quantified.Electromagnetic transient(EMT)simulations using detailed switching models are used for validation of the proposed modelling method.

Modeling the dynamic performance of transportation infrastructure using panel data model in state-space specifications

In this study,different modeling approaches used in panel data for performance forecast of transportation infrastructure are firstly reviewed,and the panel data models(PDMs)are highlighted for longitudinal data sets.The state-space specification of PDMs are proposed as a framework to formulate dynamic performance models for transportation facilities and panel data sets are used for estimation.The models could simultaneously capture the heterogeneity and update forecast through inspections.PDMs are applied to tackle the cross-section heterogeneity of longitudinal data,and PDMs in state-space forms are used to achieve the goal of updating performance forecast with new coming data.To illustrate the methodology,three classes of dynamic PDMs are presented in four examples to compare with two classes of static PDMs for a group of composite pavement sections in an airport in east China.Estimation results obtained by ordinary least square(OLS)estimator and system generalized method of moments(SGMM)are compared for two dynamic instances.The results show that the average root mean square errors of dynamic specifications are all significantly lower than those of static counterparts as prediction continues over time.There is no significant difference of prediction accuracy between state-space model and curve shifting model over a short time.In addition,SGMM does not obtain higher prediction accuracy than OLS in this case.Finally,it is recommended to specify the inspection intervals as several constants with integer multiples.

Identification of the state-space model and payload mass parameter of a flexible space manipulator using a recursive subspace tracking method

The on-orbit parameter identification of a space structure can be used for the modification of a system dynamics model and controller coefficients. This study focuses on the estimation of a system state-space model for a two-link space manipulator in the procedure of capturing an unknown object, and a recursive tracking approach based on the recursive predictor-based subspace identification(RPBSID) algorithm is proposed to identify the manipulator payload mass parameter. Structural rigid motion and elastic vibration are separated, and the dynamics model of the space manipulator is linearized at an arbitrary working point(i.e., a certain manipulator configuration).The state-space model is determined by using the RPBSID algorithm and matrix transformation. In addition, utilizing the identified system state-space model, the manipulator payload mass parameter is estimated by extracting the corresponding block matrix. In numerical simulations, the presented parameter identification method is implemented and compared with the classical algebraic algorithm and the recursive least squares method for different payload masses and manipulator configurations. Numerical results illustrate that the system state-space model and payload mass parameter of the two-link flexible space manipulator are effectively identified by the recursive subspace tracking method.

Tracking of time-evolving sound speed profiles with an auto-regressive state-space model

An approach for time-evolving sound speed profiles tracking in shallow water is discussed. The inversion of time-evolving sound speed profiles is modeled as a state-space estimation problem, which includes a state equation for predicting the time-evolving sound speed profile and a measurement equation for incorporating local acoustic measurements. In the paper, auto-regression （AR） method is introduced to obtain a high-order AR evolution model of the sound speed field time variations, and the ensemble Kalman filter is utilized to track the sound speed field. To validate the approach, the accuracy in sound speed estimation is analyzed via a numerical implementation using the ASIAEX experimental environment and the sound velocity measurement data. Compared with traditional approaches based on the state evolution represented as a random walk, simulation results show the proposed AR method can effectively reduce the tracking errors of sound speed, and still keep good tracking performance at low signal-to-noise ratios.

State-Space Equations and the First-Phase Algorithm for Signal Control of Single Intersections

State-space equations were applied to formulate the queuing and delay of traffic at a single intersection in this paper. The signal control of a single intersection was then modeled as a discrete-time optimal control problem, with consideration of the constraints of stream conflicts, saturation flow rate, minimum green time, and maximum green time. The problem cannot be solved directly due to the nonlinear constraints. However, the results of qualitative analysis were used to develop a first-phase signal control algorithm. Simulation results show that the algorithm substantially reduces the total delay compared to fixed-time control.

STATE-SPACE MODELLING OF DYNAMIC SYSTEMS IN OCEAN ENGINEERING

Pertaining to dynamic systems in general, a review is given of relations between mathematical descriptions in the frequency domain or time domain and state-space descriptions. For the analysis of hydrodynamic problems in ocean engineering wave forces may be represented by convolution integrals. The paper presents a method to construct a finite-order state-space model which represents a good approximation to such a convolution integral. The method utilizes a particular algorithm to compute the partial derivative of the exponential function of a (state-space) matrix with respect to the matrix elements. The method is applied to an example of fitting a state space model of order five to the free oscillations corresponding to wave radiation in a transient experiment with an oscillating water column.

轨道车辆垂向轮轨力时域识别对比及其机器学习修正

为了尽可能减小轨道车辆垂向轮轨力时域识别中存在的误差,以时域法为基础,开展了基于机器学习修正的轨道车辆垂向轮轨力识别研究.首先建立了车辆动力学仿真模型,获取了车辆在随机轨道激励下以250km/h速度行驶时的轴箱加速度响应和垂向轮轨力.其次,建立了Green函数法、状态空间法这2种时域法对应的动载荷识别模型,对状态空间法的初值误差进行了分析,并引入多项式拟合法修正其趋势项误差,进而对比分析了2种方法的计算精度和计算效率.然后,针对时域法存在的识别误差,提出采用NARX(nonlinear autoregressive models with exogenous inputs)模型对识别误差进行训练和预测,用于消减模型中存在的如响应观测不全与观测噪声等因素造成的影响,进而对时域法识别结果进行修正,提高识别精度.最后,通过一个10自由度轨道车辆垂向动力学模型,对方法的正确性进行了验证.研究结果表明:2种方法对轨道车辆垂向轮轨力均具有较高的识别精度,对于各轮对的识别精度各有优劣;在计算效率方面,状态空间法比Green函数法更优;经NARX模型修正的2种时域法对轨道车辆垂向轮轨力均具有很好的识别效果,识别值与正演值的Pearson相关系数大于0.99,为极强相关.基于NARX模型的机器学习误差修正方法可有效提高时域识别精度,可以为后续轨道车辆轮轨力预测提供参考,具有较强的工程运用价值.

模型信息联合校正型自抗扰控制策略

为解决微电网受到不确定扰动时,会对直-直变换器输出的电能质量产生严重影响的问题,该文提出一种模型信息联合校正型自抗扰控制技术(ADRC-MIR)。在该控制策略中,首先借助串联超前校正的思想,以比例微分校正环节对线性扩张状态观测器的扰动观测传递函数进行修正,使其可实现对总和扰动更精确的跟踪;然后,根据状态空间平均法从被控系统中提取部分模型信息,将其写入修正后的线性扩张状态观测器的系数矩阵并最终构建出ADRC-MIR;随后基于理论推导,给出改进控制器的参数整定公式及其物理意义,并从噪声抑制、扰动抑制及其频域特性等方面指出改进后的控制器可提升控制品质的原因。最后通过对比不同工况下的数值仿真验证所提控制策略的可行性与正确性。

海上风电场经交流海缆并网谐波谐振放大分析

采用交流海缆接入电网的海上风电场在电缆线路分布电容的作用下,可能出现陆上风电场不常见的谐波谐振与谐波放大现象,严重威胁到海上风电场安全可靠运行。为研究海上风电场谐波谐振机理与谐波放大影响因素,首先,建立了海上风电场输电系统与集电系统两部分的状态空间模型,并给出谐波放大倍数、谐波含量等指标的计算方法;其次,通过特征值和参与因子揭示了谐波谐振机理及关键影响因素;然后,通过根轨迹法研究了电网短路容量、高压电缆参数和风电机组并网台数对谐振模态的影响;最后,在Matlab/Simulink仿真平台搭建江苏某海上风电场.验证理论分析的有效性。

基于模块化思想的LCC-HVDC改进小信号建模及交互稳定性分析

随着电网换相型高压直流输电(line commutated converter based high voltage direct current, LCC-HVDC)技术的广泛应用,交直流混联电力系统的交互稳定性问题日益突出。首先基于状态空间平均法建立了考虑非线性换相重叠动态过程的LCC换流器传递函数模型。为适应愈加复杂的直流输电系统建模,提出利用模块化思想分别建立LCC-HVDC各子系统小信号模型,并推导了能反映交直流系统和换流器之间电气耦合特性的接口矩阵实现子系统连接,从而模块化建立精确且易于扩展的计及控制链路延时和锁相环输出相位波动的双端LCC-HVDC系统改进小信号模型。最后分析了控制系统参数和控制链路延时对系统小干扰稳定性的影响以及失稳模态的主导因素,揭示了双端LCC-HVDC系统交直流混合谐振机理及送受端交互影响具体过程。研究结果可以为系统参数设计、谐振抑制措施提供理论基础。

Predictive active control of building structures using LQR and artificial intelligence

This study presents a neural network-based model for predicting linear quadratic regulator(LQR)weighting matrices for achieving a target response reduction.Based on the expected weighting matrices,the LQR algorithm is used to determine the various responses of the structure.The responses are determined by numerically analyzing the governing equation of motion using the state-space approach.For training a neural network,four input parameters are considered:the time history of the ground motion,the percentage reduction in lateral displacement,lateral velocity,and lateral acceleration,Output parameters are LQR weighting matrices.To study the effectiveness of an LQR-based neural network(LQRNN),the actual percentage reduction in the responses obtained from using LQRNN is compared with the target percentage reductions.Furthermore,to investigate the efficacy of an active control system using LQRNN,the controlled responses of a system are compared to the corresponding uncontrolled responses.The trained neural network effectively predicts weighting parameters that can provide a percentage reduction in displacement,velocity,and acceleration close to the target percentage reduction.Based on the simulation study,it can be concluded that significant response reductions are observed in the active-controlled system using LQRNN.Moreover,the LQRNN algorithm can replace conventional LQR control with the use of an active control system.

海上风电场经柔直送出系统的虚拟导纳中频振荡抑制策略

随着柔性直流输电技术在远海风电的广泛应用,海上换流站接入远海风电场时出现了中频振荡现象,严重危害系统安全稳定运行。为此,提出了一种基于虚拟导纳的中频振荡抑制策略。首先,采用模块化状态空间法建立了海上风电场经柔直送出系统的小信号模型。然后,采用参与因子分析方法揭示了影响中频振荡的关键因素,并分析了各关键因素对中频振荡的影响特性。在此基础上,提出在柔直控制系统中添加虚拟导纳的阻尼控制策略,并基于阻尼控制器对中频、LCL振荡的差异影响划分了控制器参数的稳定域。最后,在Matlab/Simulink中搭建时域仿真模型。结果表明,所提策略在系统不同运行工况下均可有效抑制中频振荡,提高了系统稳定性。

基于混合强化学习的主动配电网故障恢复方法

针对高比例新能源接入的配电网故障恢复问题,提出一种基于混合强化学习的主动配电网故障恢复方法。首先,以故障损失最小为恢复目标、配电网安全运行要求为约束条件,构造主动配电网的故障恢复模型;其次,建立用于故障恢复的强化学习环境,根据状态空间和动作空间特点,提出一种混合强化学习方法,该方法使用竞争架构双深度Q网络算法处理离散动作空间,进行开关动作;然后,使用深度确定性策略梯度算法处理连续动作空间,调节电源出力;最后,通过IEEE33节点系统仿真实验验证所提方法的可行性和优越性。

基于AGPF的目标定位精度改善方法

针对传统遗传算法粒子滤波容易因遗传操作参数恒定不变而陷入局部最优的问题,在遗传算法粒子滤波中引入自适应方法,提出自适应遗传算法粒子滤波。根据粒子适应度的大小,动态调节遗传操作的交叉、突变概率,从而在尽可能多地保留优势粒子的同时更有效地产生新的优势粒子,跳出局部最优。将自适应遗传算法粒子滤波应用于动态目标定位模型,并将其与遗传算法粒子滤波的性能进行比较。结果表明,自适应方法的引入可以增加算法有效粒子数,有效解决算法早熟问题,改善滤波精度,对于提高动态目标定位精度是有效的。

线性自抗扰控制系统的稳定性分析方法

针对二阶线性系统和二阶线性自抗扰控制,提出了基于误差的稳定性分析方法。该方法通过观测误差、跟踪误差状态量建立闭环系统状态空间模型,借助状态空间模型的特征值分析闭环系统的收敛性,并运用李雅普诺夫法判断系统的稳定性。与基于劳斯判据的稳定性分析方法相比较,二者的分析结论一致,算例和仿真结果验证了所提方法的简单性和有效性。此外,通过仿真和蒙特卡洛实验验证了自抗扰控制相比于PID控制在跟踪性能、抗扰能力和鲁棒性等方面的优势。