A comparative study of adaptation algorithms for nonlinear system identification based on second order Volterra and bilinear polynomial filters

Nonlinear filtering techniques have recently become very popular in the field of signal processing. In this study we have considered the modeling of nonlinear systems using adaptive nonlinear Volterra filters and bilinear polynomial filters. The performance evaluation of these nonlinear filter models for the problem of nonlinear system identification has been carried out for several random input excitations and for measurement noise corrupted output signals. The coefficients of the two candidate filter models for are designed using several well known adaptive algorithms, such as least mean squares (LMS), recursive least squares (RLS), least mean p-norm (LMP), normalized LMP (NLMP), least mean absolute deviation (LMAD) and normalized LMAD (NLMAD) algorithms. Detailed simulation studies have been carried out for comparative analysis of Volterra model and bilinear polynomial filter, using these candidate adaptation algorithms, for system identification tasks and the superior solutions are determined.     

Recursive subspace identification for on-line tracking of structural modal parameter

The objective of this paper is to develop an on-line tracking of system parameter estimation and damage detection techniques using response measurements. To avoid the singular-value-decomposition in data Hankel matrix, a new subspace identification algorithm was developed. Seismic response data of a 3-story steel frame with abrupt change of inter-story stiffness from the shaking table test was used to verify the proposed recursive subspace identification (RSI) method by using both input and output measurements. With the implementation of forgetting factor in RSI method the ability of on-line damage detection of the abrupt change of structural stiffness can be enhanced. Then, the recursive stochastic subspace identification (RSSI) algorithm is also developed for continuous structural health monitor of structure by using the output-only measurements. Verification of the proposed RSSI method by using the white noise response data of a 2-story reinforced concrete frame from its low level white noise excitation was used. Discussion of the subspace identification model parameters is also investigated.     

A fast iterative recursive least squares algorithm for Wiener model identification of highly nonlinear systems

In this paper, an online identification algorithm is presented for nonlinear systems in the presence of output colored noise. The proposed method is based on extended recursive least squares (ERLS) algorithm, where the identified system is in polynomial Wiener form. To this end, an unknown intermediate signal is estimated by using an inner iterative algorithm. The iterative recursive algorithm adaptively modifies the vector of parameters of the presented Wiener model when the system parameters vary. In addition, to increase the robustness of the proposed method against variations, a robust RLS algorithm is applied to the model. Simulation results are provided to show the effectiveness of the proposed approach. Results confirm that the proposed method has fast convergence rate with robust characteristics, which increases the efficiency of the proposed model and identification approach. For instance, the FIT criterion will be achieved 92% in CSTR process where about 400 data is used.     

Identification and analysis of hydrostatic transmission system

The dynamic behavior of hydro-static transmission (HST) systems is studied experimentally and theoretically to formulate a linearized mathematical model of the HST system and a recursive identification model is then proposed. A computer-controlled test rig is developed and the system state responses are measured. The results obtained from the experimental work and the linearized models are used to build a recursive identification model in order to identify the system under study. Furthermore, comparisons among the experimental, simulated, and identified results are presented. These results show that recursive identification models are powerful tools that can be used for the identification and analysis of HST. Finally, parameter variations of the volume displacement and the motor torque are introduced to the system in order to study their effect on pressure and hydraulic motor speed.     

Online parameter identification of the asymmetrical Bouc–Wen model for piezoelectric actuators

The hysteresis of piezoelectric actuators (PAs) possesses the asymmetrical and frequency-dependent characteristics. In order to accurately model the hysteresis of a PA, an asymmetrical Bouc–Wen model is proposed and established in this paper. The recursive least-squares online identification method is used to real-time identify the parameters of the proposed model. Meanwhile, in order to avoid the data saturation phenomenon, the limited memory method is used to limit the number of the data sets. The experimental system is setup and the performance of this method is experimentally verified. Experimental results show that the proposed online identification method can effectively improve the modeling accuracy.     

机械振动结构的ARMRX建模及模态参数识别

由振动系统的运动方程建立了描述系统输入、输出和噪声特性的受控自回归滑动平均模型(ARMAX)。采用基于限定记忆的增广最小二乘算法估计其参数,克服了以往传统方法计算的复杂性,以及难以在线的缺点。仿真结果表明本文方法鲁棒性较好。     

Recursive fuzzy c-means clustering for recursive fuzzy identification of time-varying processes

In this paper we propose a new approach to on-line Takagi-Sugeno fuzzy model identification. It combines a recursive fuzzy c-means algorithm and recursive least squares. First the method is derived and than it is tested and compared on a benchmark problem of the Mackey-Glass time series with other established on-line identification methods. We showed that the developed algorithm gives a comparable degree of accuracy to other algorithms. The proposed algorithm can be used in a number of fields, including adaptive nonlinear control, model predictive control, fault detection, diagnostics and robotics. An example of identification based on a real data of the waste-water treatment process is also presented.     

Finite-time tracking control of nth-order chained-form non-holonomic systems in the presence of disturbances

This paper addresses the problem of finite-time tracking controller design for nth-order chained-form non-holonomic systems in the presence of unknown disturbances. To this aim, a generalized disturbance observer based controller is proposed and combined with a recursive terminal sliding mode approach which guarantees finite-time convergence of the disturbance observer dynamic. By introducing a time-varying transformation and introducing a new control law, the existence of the sliding around the recursive terminal sliding mode surfaces is guaranteed. Finally, the proposed approach is applied for a wheeled mobile robot with a fourth-order chained-form non-holonomic model. The simulation results demonstrate the desirable and robust tracking performance of the proposed approach in the presence of unknown disturbance.     

Free knot recursive B-spline for compensation of nonlinear smart sensors

Compensation of nonlinear smart sensors is an important topic that must always be considered to assure the accuracy of measurement systems. Nowadays, with the advent of microprocessor devices in smart sensors, advanced compensation algorithms can be implemented to improve the accuracy of measurement. In this paper, an inverse modeling methodology based on B-spline is proposed for the compensation of nonlinear smart sensors. To avoid complicated least squares solution of the B-spline, a training algorithm in a recursive form is proposed to reduce the training cost and make the on-chip training of B-spline available. Moreover, the choices of B-spline knots and training points are important designed parameters in this methodology. So the free knot insertion algorithm and training points’ selection method are used prior to the training process to improve the accuracy of the inverse models and avoid the under and over fitting. Simulations and results are presented to validate the theoretical expectations.     

Parameters identification of Van der Pol–Duffing oscillators via particle swarm optimization and differential evolution

Many of the proposed approaches for non-linear systems control are developed under the assumption that all involved parameters are known in advance. Unfortunately, their estimation is not so simple because the nature of the non-linear behaviors is very complex in the most part of the cases.In view of this complication, parameters identification of non-linear oscillators has attracted increasing interests in various research fields: from a pure mathematical point-of-view, parameters identification can be formalized as a multi-dimensional optimization problem, typically over real bounded domains. In doing this, the use of the so-called non-classical methods based on soft computing theories seems to be promising because they do not require a priori information and the robustness of the identification against the noise contamination is satisfactory. However, further studies are required to evaluate the general effectiveness of these methodologies. In this sense, the paper addresses the consistency of two classes of soft computing based methods for the identification of Van der Pol–Duffing oscillators. A large numerical investigation has been conducted to evaluate the performances of six differential evolution algorithms (including a modified differential evolution algorithm proposed by the authors) and four swarm intelligence based algorithms (including a chaotic particle swarm optimization algorithm). Single well, double well and double-hump oscillators are identified and noisy system responses are considered in order to evaluate the robustness of the identification processes. The investigated soft computing techniques behave very well and thus they are suitable for practical applications.     

Identification and adaptation of linear look-up table parameters using an efficient recursive least-squares technique

Linear look-up tables are widely used to approximate and characterize complex nonlinear functional relationships between system input and output. However, both the initial calibration and subsequent real-time adaptation of these tables can be time consuming and prone to error as a result of the large number of table parameters typically required to map the system and the uncertainties and noise in the experimental data on which the calibration is based. In this paper, a new method is presented for identifying or adapting the look-up table parameters using a recursive least-squares based approach. The new method differs from standard recursive least squares algorithms because it exploits the structure of the look-up table equations in order to perform the identification process in a way that is highly computationally and memory efficient. The technique can therefore be implemented within the constraints of typical embedded applications. In the present study, the technique is applied to the identification of the volumetric efficiency look-up table commonly used in gasoline engine fueling strategies. The technique is demonstrated on a Ford 2.0L I4 Duratec engine using time-delayed feedback from a sensor in the exhaust manifold in order to adapt the table parameters online.     

A robust H∞ learning approach to blind separation of slowly time-varying mixture of acoustic electromechanical signals

Although many techniques have been developed for solving the blind source separation (BSS) problem, some issues related to robustness of BSS algorithms are yet to be addressed. Most of the BSS algorithms developed assume the mixing system to be stationary. In this paper, we present a robust approach based on H_∞ learning to address the instantaneous BSS problem in a non-stationary mixing environment. The motivation behind applying H_∞ filter is that these are robust to errors arising out of model uncertainties, parameter variations and additive noise. Acoustic electromechanical signals have been considered for simulation purpose. Simulation results demonstrate that the H_∞ filter performs superior to Kalman filter and VS-NGA algorithm. To ensure practicability of the proposed approach, the H_∞ learning algorithm has been implemented and tested on Texas Instrument's TMS320C6713 floating point DSP platform successfully.     

Recursive newton-euler formulation for flexible dynamic manufacturing analysis of open-loop robotic systems

The main objective of this paper is to develop a recursive formulation for the flexible dynamic manufacturing analysis of open-loop robotic systems. The nonlinear generalized Newton-Euler equations are used for flexible bodies that undergo large translational and rotational displacements. These equations are formulated in terms of a set of time invariant scalars, vectors and matrices that depend on the spatial coordinates as well as the assumed displacement fields. These time invariant quantities represent the dynamic manufacturing couplings between the rigid body motion and elastic deformation. This formulation applies recursive procedures with the generalized Newton-Euler equations for flexible bodies to obtain a large, loosely coupled system equation describing motion in flexible manufacturing systems. The techniques used to solve the system equations can be implemented in any computer system. The algorithms presented in this investigation are illustrated using cylindrical joints for open-loop robotic systems, which can be easily extended to revolute, slider and rigid joints. The recursive Newton-Euler formulation developed in this paper is demonstrated with a robotic system using cylindrical mechanical joints.     

Recursive Newton–Euler formulation for flexible dynamic manufacturing analysis of open-loop robotic systems

The main objective of this paper is to develop a recursive formulation for the flexible dynamic manufacturing analysis of open-loop robotic systems. The nonlinear generalized Newton–Euler equations are used for flexible bodies that undergo large translational and rotational displacements. These equations are formulated in terms of a set of time invariant scalars, vectors and matrices that depend on the spatial coordinates as well as the assumed displacement fields. These time invariant quantities represent the dynamic manufacturing couplings between the rigid body motion and elastic deformation. This formulation applies recursive procedures with the generalized Newton–Euler equations for flexible bodies to obtain a large, loosely coupled system equation describing motion in flexible manufacturing systems. The techniques used to solve the system equations can be implemented in any computer system. The algorithms presented in this investigation are illustrated using cylindrical joints for open-loop robotic systems, which can be easily extended to revolute, slider and rigid joints. The recursive Newton–Euler formulation developed in this paper is demonstrated with a robotic system using cylindrical mechanical joints.     

Parameters identification and trajectory control for a hydraulic system

In order to improve the tracking accuracy of a hydraulic system, an improved ant colony optimization algorithm (IACO) is proposed to optimize the values of proportional–integral–derivative (PID) controller. In addition, this paper presents an experimental study on the parameters identification to deduce accurate numerical values of the hydraulic system, which also determines the relationship between control signal and output displacement. Firstly, the basic principle of the hydraulic system and the mathematical model of the electro-hydraulic proportional control system are analyzed. Based on the theoretical models, the transfer function of the control system is obtained by recursive least square identification method (RLS). Then, the key parameters of the control system model are obtained. Some improvements are proposed to avoid premature convergence and slow convergence rate of ACO: the transition probability is revised based adjacent search mechanism, dynamic pheromone evaporation coefficient adjustment strategy is adopted, pheromone update rule and parameters optimization range are also improved. Then the proposed IACO tuning based PID controller and the identification parameters are modeled and simulated using MATLAB/Simulink and AMESim co-simulation platform. Comparisons of IACO, standard ACO and Ziegler–Nichols (Z–N)PID controllers are carried out with different references as step signal and sinusoidal wave using the co-simulation platform. The simulation results of the bucket system using the proposed controller demonstrates improved settling time, rise time and the convergence speed with a new objective function J. Finally, experiments with leveling operations are performed on a 23 ton robotic excavator. The experimental results show that the proposed controller improves the trajectory accuracy of the leveling operation by 28% in comparison to the standard ACO-PID controller.     

基于指数窗截取递推最小二乘法的齿轮啮合刚度辨识算法研究

齿轮在机械传动系统中有着广泛应用,由于齿轮啮合过程中参与啮合的轮齿对数周期变化,因此,齿轮啮合刚度为时变参数,在啮合时会产生啮合振动。当齿轮副出现齿根裂纹时,啮合刚度会减小,齿轮啮合产生的系统振动响应也发生改变,通过振动响应辨识齿轮啮合刚度能够监测齿轮副的健康状态。针对齿轮啮合刚度的时变特征,提出了基于指数窗截取递推最小二乘(Exponential window recursive least square,EWRLS)算法和振动信号瞬时频率的齿轮啮合刚度辨识方法。进行啮合刚度辨识时,EWRLS算法将输入、输出齿轮的转速曲线分别作为辨识输入信号和观测信号,使用指数窗函数进行数据截断,使用递推最小二乘算法估计系统参数。为了计算输入、输出齿轮的转速曲线,使用经验模态分解(Empirical mode decomposition,EMD)方法将振动信号分解为具有不同变化频率的本征模态函数(Intrinsic mode function,IMF),并根据IMF的平均频率重构输入、输出齿轮的特征信号。通过Hilbert变换计算特征信号的瞬时频率曲线,从而获得各齿轮的转速曲线。使用仿真和实测信号对算法进行验证,结果表明,EWRLS算法能够辨识齿轮副的时变啮合刚度。     

A recursive subsystem synthesis method for repeated closed loop structure in multibody dynamics

A recursive subsystem synthesis method has been proposed for efficient analysis for a repeated closed loop structure in multibody dynamics. Virtual work form of equations of motion has been used to reduce subsystem equations of motion. Position, velocity, and acceleration analyses are carried out subsystem by subsystem in the forward recursive fashion. Effective mass matrices and force vectors are computed subsystem by subsystem in the backward recursive fashion. An excavator example is used for a repeated closed loop structure to validate the proposed method. This paper was presented at the 4th Asian Conference on Multibody Dynamics(ACMD2008), Jeju, Korea, August 20–23, 2008. Sung-Soo Kim received a B.S. degree in Agricultural Engineering from Seoul National University in 1981. He then went on to receive his M.S. and Ph.D. degrees in Mechanical Engineering from the University of Iowa in 1983 and 1988, respectively. Dr. Kim is currently a Professor in the Department of Mechatronics Engineering at Chungnam National University in Daejeon, Korea. His research interests are real-time multibody formulation and its application to the automotive systems and military robot systems.     

Simultaneous identification of residual unbalances and bearing dynamic parameters from impulse responses of rotor–bearing systems

An identification algorithm for simultaneous estimation of residual unbalances and bearing dynamic parameters by using impulse response measurements is presented for multi-degree-of-freedom (mdofs) flexible rotor–bearing systems. The algorithm identifies speed-dependent bearing dynamic parameters for each bearing and residual unbalances at predefined balancing planes. Bearing dynamic parameters consist of four stiffness and four damping coefficients and residual unbalances contain the magnitude and phase information. Timoshenko beam with gyroscopic effects are included in the system finite element modelling. To overcome the practical difficulty of number of responses that can be measured, the standard condensation is used to reduce the number of degrees of freedom (dofs) of the model. For illustration, responses in time domain are simulated due to impulse forces in the presence of residual unbalances from a rotor–bearing model and transformed to frequency domain. The identification algorithm uses these responses to estimate bearing dynamic parameters along with residual unbalances. The proposed algorithm has the flexibility to incorporate any type and any number of bearings including seals. The identification algorithm has been tested with the measurement noise in the simulated response. Identified parameters match quite well with assumed parameters used for the simulation of responses. The response reproduction capability of identified parameters has been found to be excellent.     

State and actuator fault estimation observer design integrated in a riderless bicycle stabilization system

This paper deals with an observer design for Linear Parameter Varying (LPV) systems with high-order time-varying parameter dependency. The proposed design, considered as the main contribution of this paper, corresponds to an observer for the estimation of the actuator fault and the system state, considering measurement noise at the system outputs. The observer gains are computed by considering the extension of linear systems theory to polynomial LPV systems, in such a way that the observer reaches the characteristics of LPV systems. As a result, the actuator fault estimation is ready to be used in a Fault Tolerant Control scheme, where the estimated state with reduced noise should be used to generate the control law. The effectiveness of the proposed methodology has been tested using a riderless bicycle model with dependency on the translational velocity v, where the control objective corresponds to the system stabilization towards the upright position despite the variation of v along the closed-loop system trajectories.     

压电执行器的Bouc-Wen模型在线参数辨识

现有的定参数Bouc-Wen模型由于无法表征压电执行器迟滞具有的频移和时变性,极易产生较大的模拟误差。为了精确地模拟压电执行器的迟滞特性,本文建立了压电执行器的Bouc-Wen模型,并采用递推最小二乘在线辨识方法来实时辨识Bouc-Wen模型的参数。为了避免出现数据饱和现象,使用限定记忆来限定辨识方法所使用的数据组数。为验证该辨识方法的有效性,建立了相应的实验系统对其进行实验验证。实验结果表明,限定记忆递推最小二乘在线辨识方法能使Bouc-Wen模型也呈现频移和时变特性。以100 Hz的驱动电压为例,其最大绝对模拟误差从1.38μm降为0.51μm。因此,与传统的离线参数辨识方法相比,限定记忆递推最小二乘在线辨识方法能够有效地提高Bouc-Wen模型的模拟精度。