Nonlinear Dynamic System Identification of ARX Model for Speech Signal Identification

System Identification becomes very crucial in the field of nonlinear and dynamic systems or practical systems.As most practical systems don’t have prior information about the system behaviour thus,mathematical modelling is required.The authors have proposed a stacked Bidirectional Long-Short Term Memory(Bi-LSTM)model to handle the problem of nonlinear dynamic system identification in this paper.The proposed model has the ability of faster learning and accurate modelling as it can be trained in both forward and backward directions.The main advantage of Bi-LSTM over other algorithms is that it processes inputs in two ways:one from the past to the future,and the other from the future to the past.In this proposed model a backward-running Long-Short Term Memory(LSTM)can store information from the future along with application of two hidden states together allows for storing information from the past and future at any moment in time.The proposed model is tested with a recorded speech signal to prove its superiority with the performance being evaluated through Mean Square Error(MSE)and Root Means Square Error(RMSE).The RMSE and MSE performances obtained by the proposed model are found to be 0.0218 and 0.0162 respectively for 500 Epochs.The comparison of results and further analysis illustrates that the proposed model achieves better performance over other models and can obtain higher prediction accuracy along with faster convergence speed.

IDENTIFICATION OF NONLINEAR DYNAMIC SYSTEMS:TIME-FREQUENCY FILTERING AND SKELETON CURVES

The nonlinear behavior varying with the instantaneous response was analyzed through the joint time-frequency analysis method for a class of S. D. O. F nonlinear system. A masking operator an definite regions is defined and two theorems are presented. Based on these, the nonlinear system is modeled with a special time-varying linear one, called the generalized skeleton linear system (GSLS). The frequency skeleton curve and the damping skeleton curve are defined to describe the main feature of the non-linearity as well. Moreover, an identification method is proposed through the skeleton curves and the time-frequency filtering technique.

THE ACCOMPANIED SLOWLY-VARIANT-SYSTEM OF NONLINEAR DYNAMIC SYSTEMS

The slowly-variant-system is defined and analyzed in this paper and the nonlinear relationship between its instantaneous parameters and the instantaneous amplitude and frequency of its free vibration response is established. By defining the band-pass mapping, a slowly-variant-system which we call the accompanied slowly-variant-system is extracted from the nonlinear system; and the relationship between the two systems is discussed. Also, the skeleton curves that can illustrate the nonlinearity and the main properties of the nonlinear system directly and concisely are defined. Work done in this paper opens a new way for nonlinearity detection and identification for nonlinear systems.

Identification of Artificial Neural Network Models for Three-Dimensional Simulation of a Vibration-Acoustic Dynamic System

Industrial noise can be successfully mitigated with the combined use of passive and Active Noise Control (ANC) strategies. In a noisy area, a practical solution for noise attenuation may include both the use of baffles and ANC. When the operator is required to stay in movement in a delimited spatial area, conventional ANC is usually not able to adequately cancel the noise over the whole area. New control strategies need to be devised to achieve acceptable spatial coverage. A three-dimensional actuator model is proposed in this paper. Active Noise Control (ANC) usually requires a feedback noise measurement for the proper response of the loop controller. In some situations, especially where the real-time tridimensional positioning of a feedback transducer is unfeasible, the availability of a 3D precise noise level estimator is indispensable. In our previous works [1,2], using a vibrating signal of the primary source of noise as an input reference for spatial noise level prediction proved to be a very good choice. Another interesting aspect observed in those previous works was the need for a variable-structure linear model, which is equivalent to a sort of a nonlinear model, with unknown analytical equivalence until now. To overcome this in this paper we propose a model structure based on an Artificial Neural Network (ANN) as a nonlinear black-box model to capture the dynamic nonlinear behaveior of the investigated process. This can be used in a future closed loop noise cancelling strategy. We devise an ANN architecture and a corresponding training methodology to cope with the problem, and a MISO (Multi-Input Single-Output) model structure is used in the identification of the system dynamics. A metric is established to compare the obtained results with other works elsewhere. The results show that the obtained model is consistent and it adequately describes the main dynamics of the studied phenomenon, showing that the MISO approach using an ANN is appropriate for the simulation of the investigated process. A clear conclusion is reached highlighting the promising results obtained using this kind of modeling for ANC.

Finite-Time Distributed Identification for Nonlinear Interconnected Systems

In this paper,a novel finite-time distributed identification method is introduced for nonlinear interconnected systems.A distributed concurrent learning-based discontinuous gradient descent update law is presented to learn uncertain interconnected subsystems’dynamics.The concurrent learning approach continually minimizes the identification error for a batch of previously recorded data collected from each subsystem as well as its neighboring subsystems.The state information of neighboring interconnected subsystems is acquired through direct communication.The overall update laws for all subsystems form coupled continuous-time gradient flow dynamics for which finite-time Lyapunov stability analysis is performed.As a byproduct of this Lyapunov analysis,easy-to-check rank conditions on data stored in the distributed memories of subsystems are obtained,under which finite-time stability of the distributed identifier is guaranteed.These rank conditions replace the restrictive persistence of excitation(PE)conditions which are hard and even impossible to achieve and verify for interconnected subsystems.Finally,simulation results verify the effectiveness of the presented distributed method in comparison with the other methods.

Nonlinear Systems Identification via an Input-Output Model Based on a Feedforward Neural Network

This paper develops a feedforward neural network based input output model for a general unknown nonlinear dynamic system identification when only the inputs and outputs are accessible observations. In the developed model, the size of the input space is directly related to the system order. By monitoring the identification error characteristic curve, we are able to determine the system order and subsequently an appropriate network structure for systems identification. Simulation results are promising and show that generic nonlinear systems can be identified, different cases of the same system can also be discriminated by our model.

A Local Sparse Screening Identification Algorithm with Applications

Extracting nonlinear governing equations from noisy data is a central challenge in the analysis of complicated nonlinear behaviors.Despite researchers follow the sparse identification nonlinear dynamics algorithm(SINDy)rule to restore nonlinear equations,there also exist obstacles.One is the excessive dependence on empirical parameters,which increases the difficulty of data pre-processing.Another one is the coexistence of multiple coefficient vectors,which causes the optimal solution to be drowned in multiple solutions.The third one is the composition of basic function,which is exclusively applicable to specific equations.In this article,a local sparse screening identification algorithm(LSSI)is proposed to identify nonlinear systems.First,we present the k-neighbor parameter to replace all empirical parameters in data filtering.Second,we combine the mean error screening method with the SINDy algorithm to select the optimal one from multiple solutions.Third,the time variable t is introduced to expand the scope of the SINDy algorithm.Finally,the LSSI algorithm is applied to recover a classic ODE and a bi-stable energy harvester system.The results show that the new algorithm improves the ability of noise immunity and optimal parameters identification provides a desired foundation for nonlinear analyses.

Dynamic Programming to Identification Problems

An identification problem is considered as inaccurate measurements of dynamics on a time interval are given. The model has the form of ordinary differential equations which are linear with respect to unknown parameters. A new approach is presented to solve the identification problem in the framework of the optimal control theory. A numerical algorithm based on the dynamic programming method is suggested to identify the unknown parameters. Results of simulations are exposed.

调谐惯质阻尼器动力试验和参数识别

研发了一种新型调谐惯质阻尼器(TVMD)装置,该装置分别采用电涡流与金属弹簧作为TVMD的阻尼元件与弹簧元件.首先,对该TVMD装置进行动力试验,研究其动力特性.然后,提出4种基于试验数据识别TVMD参数的方法,即峰值点拟合法、滞回曲线拟合法、时程拟合法和传递函数拟合法.动力试验结果表明:TVMD具有惯性质量放大效应和阻尼增益效应;弹簧元件和惯容元件均表现出理想的线性特性,而阻尼元件由于电涡流阻尼固有属性和TVMD装置中存在的摩擦,表现出非线性特性.参数识别结果表明:4种方法均能合理确定TVMD参数,其中,传递函数拟合法能提供用于调谐设计的等效阻尼系数,而其他3种方法能识别非线性阻尼模型的参数;滞回曲线拟合法和时程拟合法具有更高的参数识别精度,而峰值点拟合法和传递函数拟合法具有更高的计算效率.

Parameter identification of nonlinear system via a dynamic frequency approach and its energy harvester application

A dynamic frequency-based parameter identification approach is applied for the nonlinear system with periodic responses.Starting from the energy equation,the presented method uses a dynamic frequency to precisely obtain the analytical limit cycle expression of nonlinear system and utilizes it as the mathematic foundation for parameter identification.Distinguished from the time-domain approaches,the strategy of using limit cycle to describe the system response is unaffected by the influence of phase change.The analytical expression is fitted with the value sets from phase coordinates measured in periodic oscillation of the nonlinear systems,and the unknown parameters are identified with the interior-reflective Newton method.Then the performance of this identification methodology is verified by an oscillator with nonlinear stiffness and damping.Besides,numerical simulations under noisy environment also verify the efficiency and robustness of the identification procedure.Finally,we apply this parameter identification method to the modeling of a large-amplitude energy harvester,to improve the accuracy of mechanical modeling.Not surprisingly,good agreement is achieved between the experimental data and identified parameters.It also verifies that the proposed approach is less time-consuming and more accuracy in identification procedure.

不确定转子系统动力学降阶模型构建与模型散度参数辨识

在航空、航天、船舶等领域的实际工程转子系统中,广泛存在高维复杂的非线性系统。在航空发动机转子系统、燃气轮机转子系统等重点研究领域,通常还难以对高维复杂非线性系统进行直接的数据处理和分析统计。针对不确定性转子系统的模型维度较高等问题,提出了一种模型不确定性动力学降阶计算模型构建和模型散度参数辨识方法。首先,根据确定性动力学模型和静态矩阵降阶方法,完善了确定性动力学降阶模型;然后,基于随机矩阵理论和非参数动力学建模方法,提出了不确定性动力学降阶模型;最后,利用系统确定性模型的一阶临界转速、振型和实验数据,对不确定性动力学模型的散度参数进行了辨识;为了验证散度参数辨识方法的有效性,笔者又在转子实验平台上进行了实验验证。研究结果表明:实验结果与降阶之后振动响应均值的差异性较小,且与不确定性动力学模型相差不超过10%,表明所采用的理论模型在描述转子系统行为方面具备了较高的准确性和可靠性,该模型可以为深入研究模型不确定性转子系统提供参考。

基于OFRBF-Elman网络的UUV动力学模型辨识

水下无人航行器(UUV)是具有较强非线性的复杂动态系统,而神经网络具有理论上逼近任意非线性的能力;为了提高UUV的动力学模型精度,运用了基于输出反馈的RBF-Elman(OFRBF-Elman)神经网络的系统辨识方法,即对Elman神经网络进行改进,将网络输出进行延时反馈,作为输入与隐层进行联接;将径向基函数作为隐层节点的激活函数,并以线性最小二乘法调整隐层到输出层的连接权值;然后,将该方法应用于UUV空间六自由度的动力学模型辨识中;最后,通过仿真证明了该网络结构的辨识算法具有很好的逼近能力和快速的训练速度。

Aerodynamic system instability identification with sample entropy algorithm based on feature extraction

Based on the sample entropy algorithm in nonlinear dynamics,an improved sample entropy method is proposed in the aerodynamic system instability identification for the stall precursor detection based on the nonlinear feature extraction algorithm in an axial compressor.The sample entropy algorithm is an improved algorithm based on the approximate entropy algorithm,which quantifies the regularity and the predictability of data in time series.Combined with the spatial modes representing for the rotating stall in the circumferential direction,the recognition capacity of the sample entropy is displayed well on the detection of stall inception.The indications of rotating waves are extracted by the circumferential analysis from modal wave energy.The significant ascendant in the amplitude of the spatial mode is a pronounced feature well before the imminence of stall.Data processing with the spatial mode effectively avoids the problems of inaccurate identification of a single measuring point only depending on pressure.Due to the different selections of similarity tolerance,two kinds of sample entropy are obtained.The properties of the development process of the identification model show obvious mutation phenomena at the boundary of instability,which reveal the inherent characteristic in aerodynamic system.Then the dynamic difference quotient is computed according to the difference quotient criterion,after the smooth management by discrete wavelet.The rapid increase of difference quotient can be regarded as a significant feature of the system approaching the flow instability.It is proven that based on the principle of sample entropy algorithm,the nonlinear characteristic of rotating stall can be well described.The inception can be suggested by about 12-68 revolutions before the stall arrival.This prediction method presenting is accounted for the nonlinearity of the complex flow in stall,which is in a view of data fusion system of pressure for the spatial mode tracking.

挖掘机铲斗土方动力学参数辨识方法研究

为实现挖掘机的节能降耗,进行负载识别并据此进行发动机-泵-负载匹配控制是一条重要的技术途径。为此研究了一种可以对挖掘机铲斗及其土方所构成复合体的质量、质心位置和转动惯量进行辨识的方法。首先基于挖掘机工作装置构型及各执行机构液压缸压力,通过拉格朗日法构建了工作装置的动力学方程;采集挖掘机工作装置动态运行过程中的相关数据构建大的系统方程;运用牛顿迭代法求解非线性方程组,实现对参数的辨识。通过仿真生成的数据对辨识方法进行了检验,并研究了数据量及信号噪音对辨识结果的影响。

A three-dimensional nonlinear reduced-order predictive joint model

Mechanical joints can have significant effects on the dynamics of assembled structures.However,the lack of efficacious predictive dynamic models tot joints hinders accurate prediction of their dynamic behavior.The goal of our work is to develop physics-based,reduced-order,finite element models that are capable of replicating the effects of joints on vi- brating structures.The authors recently developed the so-called two-dimensional adjusted lwan beam element(2-D AIBE) to simulate the hysteretic behavior of bolted joints in 2-D beam structures.In this paper,2-D AIBE is extended to three-di- mensional cases by formulating a three-dimensional adjusted lwan beam element(3-D AIBE).hupulsive loading experi- ments are applied to a jointed frame structure and a beam structure containing the same joint.The frame is subjected to ex- citation out of plane so that the joint is under rotation and single axis bending.By assuming that the rotation in the joint is linear elastic,the parameters of the joint associated with bending in the flame are identified from acceleration responses of the jointed beam structure,using a multi-layer teed-torward neural network(MLFF).Numerieal simulation is then per- formed on the frame structure using the identified parameters.The good agreement between the simulated and experimental impulsive acceleration responses of the frame structure validates the efficacy of the presented 3-D AIBE,and indicates that the model can potentially be applied to more complex structural systems with joint parameters identified from a relatively simple structure.

Survey on nonlinear reconfigurable flight control

An overview on nonlinear reconfigurable flight control approaches that have been demonstrated in flight-test or highfidelity simulation is presented. Various approaches for reconfigurable flight control systems are considered, including nonlinear dynamic inversion, parameter identification and neural network technologies, backstepping and model predictive control approaches. The recent research work, flight tests, and potential strength and weakness of each approach are discussed objectively in order to give readers and researchers some reference. Finally, possible future directions and open problems in this area are addressed.

林木果球采收机械臂动力学参数辨识及补偿

由于林木果球采收机械臂的工作场景复杂,对机械臂控制精准度的要求越来越高,研究机械臂动力学模型对其控制精度的影响非常重要。为提升机械臂的控制精度,提出一种在优化后的激励轨迹下基于最小二乘法和高斯混合模型(GMM)的3次迭代整体参数辨识方法。该方法以6自由度机械臂构型为例,通过建立动力学模型及QR(正交三角)分解得到最小参数集;通过轨迹优化算法得到激励轨迹的优化参数,进而得到优化的激励轨迹;得到轨迹后,依次对关节力矩采用迭代加权最小二乘法进行理论辨识,构建区分关节高、低速的非线性模型对机械臂非线性摩擦力进行拟合,用GMM算法来补偿无法精确建模的不确定力矩分量。在COMAN R5机械臂上进行试验测试,结果表明,所提出的轨迹参数优化方法将条件数从329减少到193,力矩残差的平均均方根从9.53降低到6.14,从而证明激励轨迹和辨识方案的可行性和有效性。

采用重构吸引子的辐射源个体识别技术

为解决现有基于相空间个体识别方法面临重构特征矢量维数高、计算效率低、鲁棒性差等问题,从非线性动力学角度出发,构建了基于重构吸引子的辐射源个体识别框架,并在此框架内提出了基于等距映射的辐射源个体识别技术。该技术采用等距映射从相空间中重构辐射源吸引子,可以更低的维度描述辐射源系统动力学特性,反映辐射源个体的“指纹”特征。实验表明该方法识别准确率更高、效率更高、听鲁棒性更强。

基于GWO-BP方法的加速度计动态模型研究

针对高g值加速度计动态模型问题,基于Hopkinson杆的校准系统所测的输入输出数据建立系统模型,提出了GWO-BP神经网络动态建模方法。利用灰狼种群算法优化BP神经网络建立的加速度计动态模型,对模拟输入输出信号进行仿真。最后,利用Hopkinson杆标定系统对加速度计的输入输出进行实测。结果表明,相比于BP神经网络算法,该算法经过优化改进后,求解精度提高了43.6%,证明了该方法的可行性。

基于相空间重构的辐射源个体识别技术综述

辐射源个体识别技术,起源于雷达目标精确辨识任务,旨在根据截获的电磁信号提取辐射源独有的指纹特征,并进一步辨识辐射源个体身份的技术。相空间重构技术,作为一种有效的时间序列分析技术,可以从一维时间序列中重构一个与原系统非线性动力学特性相同的相空间。相空间重构技术自2007年开始被诸多学者引入辐射源个体识别问题中。然而,该项技术研究时间较短且分布较为分散,尚未形成清楚的发展脉络。对此,该文旨在系统性地总结归纳基于相空间重构的辐射源个体识别技术。首先,在介绍相空间重构技术的基础上,论述了相空间重构技术应用于辐射源个体识别的理论依据。其次,从方法框架、算法分类、算法应用效果、算法初步对比4个维度,介绍了基于相空间重构技术的辐射源个体识别技术的研究现状。仿真实验结果表明,该项技术能够有效地捕捉辐射源硬件的非理想性,胜任目标精确辨识任务,并可通过特征融合等手段提升算法鲁棒性。最后,总结现有方法的不足并展望其未来发展前景。