Showing papers on "System identification published in 2013"

Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains

Abstract: The NARMAX (nonlinear autoregressive moving average with exogenous inputs) model The orthogonal least squares algorithm that allows models to be built term by term where the error reduction ratio reveals the percentage contribution of each model term Statistical and qualitative model validation methods that can be applied to any model class Generalised frequency response functions which provide significant insight into nonlinear behaviours A completely new class of filters that can move, split, spread, and focus energy The response spectrum map and the study of sub harmonic and severely nonlinear systems Algorithms that can track rapid time variation in both linear and nonlinear systems The important class of spatio–temporal systems that evolve over both space and time Many case study examples from modelling space weather, through identification of a model of the visual processing system of fruit flies, to tracking causality in EGG data are all included to demonstrate how easily the methods can be applied in practice and to show the insight that the algorithms reveal even for complex systems

Hankel Matrix Rank Minimization with Applications to System Identification and Realization

Abstract: We introduce a flexible optimization framework for nuclear norm minimization of matrices with linear structure, including Hankel, Toeplitz, and moment structures and catalog applications from diverse fields under this framework. We discuss various first-order methods for solving the resulting optimization problem, including alternating direction methods of multipliers, proximal point algorithms, and gradient projection methods. We perform computational experiments to compare these methods on system identification problems and system realization problems. For the system identification problem, the gradient projection method (accelerated by Nesterov's extrapolation techniques) and the proximal point algorithm usually outperform other first-order methods in terms of CPU time on both real and simulated data, for small and large regularization parameters, respectively, while for the system realization problem, the alternating direction method of multipliers, as applied to a certain primal reformulation, usuall...

l_0 Norm Constraint LMS Algorithm for Sparse System Identification

Abstract: In order to improve the performance of Least Mean Square (LMS) based system identification of sparse systems, a new adaptive algorithm is proposed which utilizes the sparsity property of such systems. A general approximating approach on norm—a typical metric of system sparsity, is proposed and integrated into the cost function of the LMS algorithm. This inte- gration is equivalent to add a zero attractor in the iterations, by which the convergence rate of small coefficients, that dominate the sparse system, can be effectively improved. Moreover, using par- tial updating method, the computational complexity is reduced. The simulations demonstrate that the proposed algorithm can effectively improve the performance of LMS-based identification algorithms on sparse system. IndexTerms— norm, adaptivefilter, least meansquare (LMS), sparsity.

Adaptive time series compensator for delay compensation of servo-hydraulic actuator systems for real-time hybrid simulation

Abstract: SUMMARY Hydraulic actuators are typically used in a real-time hybrid simulation to impose displacements to a test structure (also known as the experimental substructure). It is imperative that good actuator control is achieved in the real-time hybrid simulation to minimize actuator delay that leads to incorrect simulation results. The inherent nonlinearity of an actuator as well as any nonlinear response of the experimental substructure can result in an amplitude-dependent behavior of the servo-hydraulic system, making it challenging to accurately control the actuator. To achieve improved control of a servo-hydraulic system with nonlinearities, an adaptive actuator compensation scheme called the adaptive time series (ATS) compensator is developed. The ATS compensator continuously updates the coefficients of the system transfer function during a real-time hybrid simulation using online real-time linear regression analysis. Unlike most existing adaptive methods, the system identification procedure of the ATS compensator does not involve user-defined adaptive gains. Through the online updating of the coefficients of the system transfer function, the ATS compensator can effectively account for the nonlinearity of the combined system, resulting in improved accuracy in actuator control. A comparison of the performance of the ATS compensator with existing linearized compensation methods shows superior results for the ATS compensator for cases involving actuator motions with predefined actuator displacement histories as well as real-time hybrid simulations. Copyright © 2013 John Wiley & Sons, Ltd.

State of Charge Estimation Using the Extended Kalman Filter for Battery Management Systems Based on the ARX Battery Model

Abstract: State of charge (SOC) is a critical factor to guarantee that a battery system is operating in a safe and reliable manner. Many uncertainties and noises, such as fluctuating current, sensor measurement accuracy and bias, temperature effects, calibration errors or even sensor failure, etc. pose a challenge to the accurate estimation of SOC in real applications. This paper adds two contributions to the existing literature. First, the auto regressive exogenous (ARX) model is proposed here to simulate the battery nonlinear dynamics. Due to its discrete form and ease of implemention, this straightforward approach could be more suitable for real applications. Second, its order selection principle and parameter identification method is illustrated in detail in this paper. The hybrid pulse power characterization (HPPC) cycles are implemented on the 60AH LiFePO4 battery module for the model identification and validation. Based on the proposed ARX model, SOC estimation is pursued using the extended Kalman filter. Evaluation of the adaptability of the battery models and robustness of the SOC estimation algorithm are also verified. The results indicate that the SOC estimation method using the Kalman filter based on the ARX model shows great performance. It increases the model output voltage accuracy, thereby having the potential to be used in real applications, such as EVs and HEVs.

Bayesian Inference and Learning in Gaussian Process State-Space Models with Particle MCMC

Abstract: State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference \emph{and learning} (i.e. state estimation and system identification) in nonlinear nonparametric state-space models. We place a Gaussian process prior over the state transition dynamics, resulting in a flexible model able to capture complex dynamical phenomena. To enable efficient inference, we marginalize over the transition dynamics function and infer directly the joint smoothing distribution using specially tailored Particle Markov Chain Monte Carlo samplers. Once a sample from the smoothing distribution is computed, the state transition predictive distribution can be formulated analytically. Our approach preserves the full nonparametric expressivity of the model and can make use of sparse Gaussian processes to greatly reduce computational complexity.

Integrated System Identification and State-of-Charge Estimation of Battery Systems

Abstract: Accurate estimation of the state of charge in battery systems is of essential importance for battery system management. Due to nonlinearity, high sensitivity of the inverse mapping from external measurements, and measurement errors, SOC estimation has remained a challenging task. This is further compounded by the fact that battery characteristic model parameters change with time and operating conditions. This paper introduces an adaptive nonlinear observer design that compensates nonlinearity and achieves better estimation accuracy. A two-time-scale signal processing method is employed to attenuate the effects of measurement noises on SOC estimates. The results are further expanded to derive an integrated algorithm to identify model parameters and initial SOC jointly. Simulations were performed to illustrate the capability and utility of the algorithms. Experimental verifications are conducted on Li-ion battery packs of different capacities under different load profiles.

Application of Several Data-Driven Techniques for Predicting Groundwater Level

Abstract: In this study, several data-driven techniques including system identification, time series, and adaptive neuro-fuzzy inference system (ANFIS) models were applied to predict groundwater level for different forecasting period. The results showed that ANFIS models out-perform both time series and system identification models. ANFIS model in which preprocessed data using fuzzy interface system is used as input for artificial neural network (ANN) can cope with non-linear nature of time series so it can perform better than others. It was also demonstrated that all above mentioned approaches could model groundwater level for 1 and 2 months ahead appropriately but for 3 months ahead the performance of the models was not satisfactory.

System Identification for Small, Low-Cost, Fixed-Wing Unmanned Aircraft

Abstract: This paper describes a practical system identification procedure for small, low-cost, fixed-wing unmanned aircraft. Physical size and cost restrictions limit the sensing capabilities of these vehicles. The procedure is demonstrated on an Ultra Stick 25e, therefore emphasizing a minimum complexity approach compatible with a low-cost inertial sensor. A linear model, obtained from the generic nonlinear equations of motion for aircraft, is used as a basis for system identification. This model is populated with results from a first principles analysis to form a baseline model. Flight experiments are designed using the baseline model and operational constraints to collect informative data. Parameters of the linear model are identified by fitting the model to frequency responses extracted from the data. The parameters are integrated into the nonlinear equations of motion, and both linear and nonlinear models are validated in the time domain. Verification of model accuracy is extended with a sensitivity and resid...

Intelligent Local Area Signals Based Damping of Power System Oscillations Using Virtual Generators and Approximate Dynamic Programming

Abstract: This paper illustrates the development of an intelligent local area signals based controller for damping low-frequency oscillations in power systems. The controller is trained offline to perform well under a wide variety of power system operating points, allowing it to handle the complex, stochastic, and time-varying nature of power systems. Neural network based system identification eliminates the need to develop accurate models from first principles for control design, resulting in a methodology that is completely data driven. The virtual generator concept is used to generate simplified representations of the power system online using time-synchronized signals from phasor measurement units at generating stations within an area of the system. These representations improve scalability by reducing the complexity of the system “seen” by the controller and by allowing it to treat a group of several synchronous machines at distant locations from each other as a single unit for damping control purposes. A reinforcement learning mechanism for approximate dynamic programming allows the controller to approach optimality as it gains experience through interactions with simulations of the system. Results obtained on the 68-bus New England/New York benchmark system demonstrate the effectiveness of the method in damping low-frequency inter-area oscillations without additional control effort.

Mode shape estimation algorithms under ambient conditions: A comparative review

Abstract: This paper provides a comparative review of five existing ambient electromechanical mode shape estimation algorithms, i.e., the Transfer Function (TF), Spectral, Frequency Domain Decomposition (FDD), Channel Matching, and Subspace Methods. It is also shown that the TF Method is a general approach to estimating mode shape and that the Spectral, FDD, and Channel Matching Methods are actually special cases of it. Additionally, some of the variations of the Subspace Method are reviewed and the Numerical algorithm for Subspace State Space System IDentification (N4SID) is implemented. The five algorithms are then compared using data simulated from a 17-machine model of the Western Electricity Coordinating Council (WECC) under ambient conditions with both low and high damping, as well as during the case where ambient data is disrupted by an oscillatory ringdown. The performance of the algorithms is compared using the statistics from Monte Carlo simulations and results from measured WECC data, and a discussion of the practical issues surrounding their implementation, including cases where power system probing is an option, is provided. The paper concludes with some recommendations as to the appropriate use of the various techniques.

Optimal waveform for fast entrainment of weakly forced nonlinear oscillators.

Abstract: The entrainment process is fundamental to numerous scientific and engineering applications in which oscillating systems are asymptotically synchronized to an external periodic signal [1,2]. The ability to optimize entrainment has important implications for achieving rapid cardiac resynchronization [3] and quick adjustment from jet lag [4], maximizing the growth rate of plants [5], and implementing phase-locked loop circuits and injection-locked microintegrated oscillators [6]. When the weak perturbation approximation is made, a rescaling of the phase response curve (PRC) was shown to be the minimum energy signal for spiking or entraining oscillators at a given period [7–9], and a weighted sum of appropriately shifted PRCs maximizes the range of frequency detunings for which entrainment occurs [10,11]. An alternative essential objective is to minimize the time to entrainment at a given forcing signal energy, in order to establish a fixed phase relationship between the system and forcing signal as soon as possible after the forcing is applied [12]. This notion of fast entrainment can also be used to minimize the time required to reestablish entrainment after interruptions caused by disturbances [13]. In this Letter, we use phase model reduction to derive an asymptotically optimal waveform that maximizes the average rate of entrainment for general weakly forced nonlinear oscillators. The rate of entrainment is characterized by the coefficient of exponential decay in the phase difference between the system and forcing signal. We present a theory by which the entrainment time scale is minimized for a specified forcing energy, where the optimal waveform is a sum of the PRC and its derivative with weights that depend on the difference between the natural and forcing frequencies. These findings can be applied to weakly nonlinear oscillators just past the Hopf bifurcation, as well as strongly nonlinear relaxation oscillators. We confirm our results with numerical simulations using the Hodgkin-Huxley (HH) neuron model, as well as in experiments on an oscillatory chemical system arising through the electrodissolution of nickel in sulfuric acid. Phase coordinate transformation is a model reduction technique that is useful for examining nonlinear oscillating systems [14,15], and can also be used for system identification when the dynamics are complex or unknown [2]. Such models have been studied extensively, with a particular focus on neural [14,16] and electrochemical [17–19] systems. Consider a full state-space model described by a smooth ordinary differential equation system _ x ¼ fðx; uÞ,

Non-Uniform Norm Constraint LMS Algorithm for Sparse System Identification

Abstract: Sparsity property has long been exploited to improve the performance of least mean square (LMS) based identification of sparse systems, in the form of l0-norm or l1-norm constraint. However, there is a lack of theoretical investigations regarding the optimum norm constraint for specific system with different sparsity. This paper presents an approach by seeking the tradeoff between the sparsity exploitation effect of norm constraint and the estimation bias it produces, from which a novel algorithm is derived to modify the cost function of classic LMS algorithm with a non-uniform norm (p-norm like) penalty. This modification is equivalent to impose a sequence of l0-norm or l1-norm zero attraction elements on the iteration according to the relative value of each filter coefficient among all the entries. The superiorities of the proposed method including improved convergence rate as well as better tolerance upon different sparsity are demonstrated by numerical simulations.

Three free data sets for development and benchmarking in nonlinear system identification

Abstract: System identification is a fundamentally experimental field of science in that it deals with modeling of system dynamics using measured data. Despite this fact many algorithms and theoretical results are only tested with simulations at the time of publication. One reason for this may be a lack of easily available live data. This paper therefore presents three sets of data, suitable for development, testing and benchmarking of system identification algorithms for nonlinear systems. The data sets are collected from laboratory processes that can be described by block - oriented dynamic models, and by more general nonlinear difference and differential equation models. All data sets are available for free download.