Identification Of Time-varying Systems Research Articles

Adaptive Intelligent Inverse Control Of Nonlinear Systems With Regard To Sensor Noise And Parameter Uncertainty (Magnetic Ball Levitation System Case Study)

Abstract Type-2 Fuzzy Neural Networks have tremendous capability in identification and control of nonlinear, time-varying and uncertain systems. In this paper the procedure of designing inverse adaptive type-2 fuzzy neural controller for online control of nonlinear dynamical systems will be presented. At first the structure of a novel class of Interval Type-2 Nonlinear Takagi-Sugeno-Keng Fuzzy Neural Networks (IT2-NTSK-FNN) will be presented. There is a class of nonlinear function of inputs in the consequent part of fuzzy rules. This IT2-NTSK-FNN comprises seven layers and the fuzzification is done in two first layers including type-2 fuzzy neurons with uncertainties in the mean of Gaussian membership functions. Third layer is rule layer and model reduction occurs in fourth layer via adaptive nodes. Fifth, sixth and seventh layers are consequent layer, centroid rules’ calculation layer and output layer respectively. For training the network backpropagation (steepest descend) method with adaptive training rate is used. Finally, three methods including online adaptive inverse controller based on IT2-NTSK-FNN, IT2-TSK-FNN (linear consequent part) and Adaptive Neuro-Fuzzy Inference System (ANFIS) are employed to control of a magnetic ball levitation system. External disturbances and uncertainty in parameters are considered in the model of magnetic ball levitation system. Simulation results show the efficacy of the proposed method

A general extended Kalman filter for simultaneous estimation of system and unknown inputs

The traditional Extended Kalman filter (EKF) is a useful tool for structural parameter identification with limited observations. It is, however, not applicable when the excitations on the structure are unknown or the excitation locations are not monitored. A novel Extended Kalman filter approach referred to as the General Extended Kalman filter with unknown inputs (GEKF-UI) is proposed to estimate the structural parameters and the unknown excitations (inputs) simultaneously. The proposed GEKF-UI gives an analytical EKF solution dealing with the more general measurement scenarios with the existing EKF methods as its special cases. Existing constraints on sensor configuration have been removed enabling more general application to complex structures. Simulation results from a 3-storey linear damped shear building, an ASCE benchmark structure and a two-storey planar frame structure are used to validate the proposed method for both time-invariant and time-varying system identification.

Identification of time-varying systems using multi-scale radial basis function

Identification of time-varying systems using multi-scale radial basis function

Introducing an Evolving Local Neuro-Fuzzy Model – Application to modeling of car-following behavior

This paper proposes an Evolving Local Linear Neuro-Fuzzy Model for modeling and identification of nonlinear time-variant systems which change their nature and character over time. The proposed approach evolves through time to follow the structural changes in the time-variant dynamic systems. The evolution process is managed by a distance-based extended hierarchical binary tree algorithm, which decides whether the proposed evolving model should be adapted to the system variations or evolution is necessary. To represent an interesting but challenging example of the systems with changing dynamics, the proposed evolving model is applied to model car-following process in a traffic flow, as an online identification problem. Results of simulations demonstrate effectiveness of the proposed approach in modeling of the time-variant systems.

Moving Kriging shape function modeling of vector TARMA models for modal identification of linear time-varying structural systems

This work proposes a Moving Kriging (MK) shape function modeling method for modal identification of linear time-varying (LTV) structural systems based on vector time-dependent autoregressive moving average (VTARMA) models. It aims to avoid the functional subspaces selection of the conventional functional series VTARMA (FS-VTARMA) models. Instead of the common basis functions, it constructs the time-varying coefficients on the time nodes with the MK shape functions in a compact support domain. The merit of the MK shape function is to determine its shape parameters upon vector random vibration signals adaptively. Model identification is effectively dealt with through an optimization scheme that decomposes the identification problem into two subproblems: estimating model parameters via two-stage least squares (2SLS) method and estimating shape function parameters via a discrete-continuous-variable hybrid optimization. In addition, the model order selection is achieved by the optimization scheme. This method has been validated by a Monte Carlo study of simulation case and further by an experimental test case, and the performance and potential advantages are illustrated.

Iterative Learning Identification for Linear Time-Varying Systems

This brief presents an approach for identifying the parameters of linear time-varying systems that repeat their trajectories. The identification is based on the concept that parameter identification results can be improved by incorporating information learned from previous executions. The learning laws for this iterative learning identification are determined through an optimization framework. The convergence analysis of the algorithm is presented along with the experimental results to demonstrate its effectiveness. The algorithm is demonstrated to be capable of simultaneously estimating rapidly varying parameters and addressing robustness to noise by adopting a time-varying design approach.

Identification of nonlinear time-varying systems using an online sliding-window and common model structure selection (CMSS) approach with applications to EEG

The identification of nonlinear time-varying systems using linear-in-the-parameter models is investigated. An efficient common model structure selection (CMSS) algorithm is proposed to select a common model structure, with application to EEG data modelling. The time-varying parameters for the identified common-structured model are then estimated using a sliding-window recursive least squares (SWRLS) approach. The new method can effectively detect and adaptively track and rapidly capture the transient variation of nonstationary signals, and can also produce robust models with better generalisation properties. Two examples are presented to demonstrate the effectiveness and applicability of the new approach including an application to EEG data.

Identification of Linear Time-Varying Systems Through Waveform Diversity

Linear, time-varying (LTV) systems composed of time shifts, frequency shifts, and complex amplitude scalings are operators that act on continuous finite-energy waveforms. This paper presents a novel, resource-efficient method for identifying the parametric description of such systems, i.e., the time shifts, frequency shifts, and scalings, from the sampled response to linear frequency modulated (LFM) waveforms, with emphasis on the application to radar processing. If the LTV operator is probed with a sufficiently diverse set of LFM waveforms, then the system can be identified with high accuracy. In the case of noiseless measurements, the identification is perfect, while in the case of noisy measurements, the accuracy is inversely proportional to the noise level. The use of parametric estimation techniques with recently proposed denoising algorithms allows the estimation of the parameters with high accuracy.

A condition assessment method for time-variant structures with incomplete measurements

The structural damage incurred in a seismic event is always time-variant. In this paper, a new time-variant structural system identification method is proposed based on a two-stage strategy and incomplete structural acceleration responses. In the first stage, an external excitation identification method is developed for a time-variant structural system. The unknown structural response could be re-constructed with the average acceleration discrete algorithm in this stage. In the second stage, structural parameter is identified and updated with a reduced extended Kalman filter which can improve the computational effort. The re-constructed structural response and identified external excitation are used in the second stage for the damage identification and model updating. The proposed method is validated numerically with the simulation of a fifteen-storey shear frame structure subject to earthquake excitation. A model of a fourteen-storey concrete shear wall building was also studied experimentally with shaking table tests to further validate the proposed method. This shear wall building has a two-storey steel frame on top with base isolation. Both the stiffness of the model and the interface force in the isolator at the bottom of the steel frame during the seismic excitation were estimated with the proposed method. Results from both numerical simulations and laboratory tests indicate that the proposed method can be used to identify structural parameters and external excitations effectively based on a few number of polluted structural acceleration measurements.

A Non-Parametric Linear Parameter Varying Approach for Identification of Linear Time-Varying Systems

This paper presents a novel, non-parametric, linear parameter varying (LPV) algorithm for identification of linear time-varying systems. The method estimates the timevarying impulse response function as a LPV Laguerre basis expansion whose coefficients are functions of a scheduling variable (SV). Unlike many parametric LPV identification techniques, the method requires no a priori knowledge of the system order. Monte Carlo simulations of a time-varying, second-order system mimicking variations of reex stiffness dynamics with ankle position demonstrated that the method performs very well. It will be a valuable tool for identification of physiological and engineering systems in conditions where the system order is unknown and its parameters change with a SV.

Nonlinear Time-varying Systems Identification Based on Multi-dimensional Taylor Network and Variable Forgetting Factor Recursive Least Squares Algorithm

A novel method for nonlinear time-varying systems identification based on multi-dimensional Taylor network and variable forgetting factor recursive least squares algorithm is proposed. In this paper, the connection weight coefficients of multi-dimensional Taylor network are regarded as time-varying parameters, which are trained by the variable forgetting factor recursive least squares algorithm, to reflect the input-output change of nonlinear time-varying systems. Simulation results show that the method proposed in this paper is valid.

Clipped LMS/RLS Adaptive Algorithms: Analytical Evaluation and Performance Comparison with Low-Complexity Counterparts

The high computational load of conventional adaptive FIR filters applied to long system identification and their weak tracking ability has encouraged researchers to seek for efficient adaptive algorithms for this kind of applications. One of the efficient solutions is the three-level clipped LMS/RLS adaptive algorithm. In this paper, an insight into the performance of these adaptive algorithms that evaluates the amount of steady-state misalignment error of clipped LMS/RLS adaptive algorithms employed for identification of time-invariant and time-varying systems, is presented. Employing it, we compare the misalignment performance with their low-complexity adaptive algorithm counterparts theoretically. In addition, we derive the optimal step size/forgetting factor explicitly and also obtain a relation between the optimal level of the clipping and step size/forgetting factor to achieve the lowest steady-state misalignment and then we explain as to how to improve the performance of these kinds of adaptive algorithms by adjusting the clipping threshold according to the noise level in such a way that a higher performance is achieved. Finally, different adaptive algorithms have been further coded in VHDL in order to evaluate them in terms of speed and hardware resources.

Modal Parameters Identification of Time-Varying System Based on Hilbert-Huang Transform

Mass distribution of floating structures will change due to such factors as ballast water management during ship sailing or inward and outward port, crane movement during construction, and the loading and unloading of cargoes on the offshore platform structures, which will then make its natural frequency change with time. While traditional modal identification cannot deal with the issues of non-stationary of time-varying system, Hilbert-Huang transform is quite effective for the processing and analysis of non-stationary signal. Therefore, this paper investigates the identification of linear time-varying system using the Hilbert-Huang transform, and conducts a numerical simulation of the two degrees-of-freedom time-varying system. In addition, this paper designs a cantilever beam subjected to a moving mass, and then makes a comparison of the identification results between the present identification method and those from finite element method (FEM) and eigensystemrealization algorithm (ERA), which shows a higher accuracy of the present method for modal identification of time-varying system.

Time-Varying Ankle Mechanical Impedance During Human Locomotion.

In human locomotion, we continuously modulate joint mechanical impedance of the lower limb (hip, knee, and ankle) either voluntarily or reflexively to accommodate environmental changes and maintain stable interaction. Ankle mechanical impedance plays a pivotal role at the interface between the neuro-mechanical system and the physical world. This paper reports, for the first time, a characterization of human ankle mechanical impedance in two degrees-of-freedom simultaneously as it varies with time during walking. Ensemble-based linear time-varying system identification methods implemented with a wearable ankle robot, Anklebot, enabled reliable estimation of ankle mechanical impedance from the pre-swing phase through the entire swing phase to the early-stance phase. This included heel-strike and toe-off, key events in the transition from the swing to stance phase or vice versa. Time-varying ankle mechanical impedance was accurately approximated by a second order model consisting of inertia, viscosity, and stiffness in both inversion-eversion and dorsiflexion-plantarflexion directions, as observed in our previous steady-state dynamic studies. We found that viscosity and stiffness of the ankle significantly decreased at the end of the stance phase before toe-off, remained relatively constant across the swing phase, and increased around heel-strike. Closer investigation around heel-strike revealed that viscosity and stiffness in both planes increased before heel-strike occurred. This finding is important evidence of "pretuning" by the central nervous system. In addition, viscosity and stiffness were greater in the sagittal plane than in the frontal plane across all subgait phases, except the early stance phase. Comparison with previous studies and implications for clinical study of neurologically impaired patients are provided.

Methods for identification and optimization in intelligent systems

The paper presents several algorithms for identification, describing complex objects or control system, including: an algorithm for identification of linear time-varying control systems, multi-row algorithm for decision-making by the method of group record of arguments and neuropackage to solve the problem of functions approximation

Adaptive Polynomial Filtering using Generalized Variable Step-Size Least Mean pth Power (LMP) Algorithm

This correspondence presents the adaptive polynomial filtering using the generalized variable step-size least mean $$p$$ p th power (GVSS-LMP) algorithm for the nonlinear Volterra system identification, under the $$\alpha $$ ? -stable impulsive noise environment. Due to the lack of finite second-order statistics of the impulse noise, we espouse the minimum error dispersion criterion as an appropriate metric for the estimation error, instead of the conventional minimum mean square error criterion. For the convergence of LMP algorithm, the adaptive weights are updated by adjusting $$p\ge 1$$ p ? 1 in the presence of impulsive noise characterized by $$1<\alpha <2$$ 1 < ? < 2 . In many practical applications, the autocorrelation matrix of input signal has the larger eigenvalue spread in the case of nonlinear Volterra filter than in the case of linear finite impulse response filter. In such cases, the time-varying step-size is an appropriate option to mitigate the adverse effects of eigenvalue spread on the convergence of LMP adaptive algorithm. In this paper, the GVSS updating criterion is proposed in combination with the LMP algorithm, to identify the slowly time-varying Volterra kernels, under the non-Gaussian $$\alpha $$ ? -stable impulsive noise scenario. The simulation results are presented to demonstrate that the proposed GVSS-LMP algorithm is more robust to the impulsive noise in comparison to the conventional techniques, when the input signal is correlated or uncorrelated Gaussian sequence, while keeping $$1<p<\alpha <2$$ 1 < p < ? < 2 . It also exhibits flexible design to tackle the slowly time-varying nonlinear system identification problem.

Wavelet-based modal analysis for time-variant systems

The paper presents algorithms for modal identification of time-variant systems. These algorithms utilise the wavelet-based Frequency Response Function, and lead to estimation of all three modal parameters, i.e. natural frequencies, damping and mode shapes. The method presented utilises random impact excitation and signal post-processing based on the crazy climbers Algorithm. The method is validated using simulated and experimental data from vibration time-variant systems. The results show that the method captures correctly the dynamics of the analysed systems, leading to correct modal parameter identification.

Particle filter-based robust adaptive control for closed-loop administration of sodium nitroprusside

Automatic closed-loop administration of medicinal drugs has been the subject of intense research for decades due to its undisputed potential benefits in terms of cost savings and improved patient outcomes. However, concerns still exist about the ultimate safety of engineered feedback controllers. Manual methods remain dominant in clinical practice. In this context, we present a novel feedback control architecture, which combines multiple robust controllers with a particle filter-based method for real-time tracking of a patient’s dose-response characteristic. The proposed method is applied to the case of the drug sodium nitroprusside, a vasodepressor used in the treatment of acute hypertension in intensive care and surgery, which is modelled as having a linear-time-varying dose-response characteristic. Our design takes into account the uncertainty in the patient response parameters, as well as potential nonzero-mean disturbances in the baseline arterial pressure and several possible time trends in the variation of the dose-response model. The performance and safety of the new approach are evaluated through an extensive computational simulation campaign. The results show that the proposed system can achieve adequate and safe feedback control of mean arterial pressure, thus validating our analysis and design. Our findings also highlight the fundamental - and possibly clinically overlooked - role of system excitation in ensuring that successful simultaneous identification and control of time-varying drug administration systems can be achieved.

Recursive identification of time-varying systems: Self-tuning and matrix RLS algorithms

In this paper, a new parallel adaptive self-tuning recursive least squares (RLS) algorithm for time-varying system identification is first developed. Regularization of the estimation covariance matrix is included to mitigate the effect of non-persisting excitation. The desirable forgetting factor can be self-tuning estimated in both non-regularization and regularization cases. We then propose a new matrix forgetting factor RLS algorithm as an extension of the conventional RLS algorithm and derive the optimal matrix forgetting factor under some reasonable assumptions. Simulations are given which demonstrate that the performance of the proposed self-tuning and matrix RLS algorithms compare favorably with two improved RLS algorithms recently proposed in the literature.

Real-Time Identification of Time-Varying ARMAX Systems Based on Recursive Update of Its Parameters

A new method for identification of time-varying ARMAX systems is introduced. This method is based on expansion of time-varying parameters of the ARMAX model onto a set of basis functions. A recursive formulation for updating the coefficients of the basis functions of the time-varying parameters of the system is proposed. Similar to non-real-time basis-function methods, the proposed real-time method has the capability of tracking fast changes in the parameters of a time-varying system much better than the standard Kalman and recursive least-squares (RLS) methods. A computationally efficient version of the algorithm is also presented with a small degradation in tracking properties of the original algorithm. Selection of different types of basis functions makes the new method very flexible for different applications.