Showing papers on "System identification published in 2004"

Missing point estimation in models described by proper orthogonal decomposition

Abstract: This paper presents a new method of missing point estimation (MPE) to derive efficient reduced-order models for large-scale parameter-varying systems. Such systems often result from the discretization of nonlinear partial differential equations. A projection-based model reduction framework is used where projection spaces are inferred from proper orthogonal decompositions of data-dependent correlation operators. The key contribution of the MPE method is to perform online computations efficiently by computing Galerkin projections over a restricted subset of the spatial domain. Quantitative criteria for optimally selecting such a spatial subset are proposed and the resulting optimization problem is solved using an efficient heuristic method. The effectiveness of the MPE method is demonstrated by applying it to a nonlinear computational fluid dynamic model of an industrial glass furnace. For this example, the Galerkin projection can be computed using only 25% of the spatial grid points without compromising the accuracy of the reduced model.

Particle methods for change detection, system identification, and control

Abstract: Particle methods are a set of powerful and versatile simulation-based methods to perform optimal state estimation in nonlinear non-Gaussian state-space models. The ability to compute the optimal filter is central to solving important problems in areas such as change detection, parameter estimation, and control. Much recent work has been done in these areas. The objective of this paper is to provide a detailed overview of them.

Nonlinear dynamical system identification from uncertain and indirect measurements

Abstract: We review the problem of estimating parameters and unobserved trajectory components from noisy time series measurements of continuous nonlinear dynamical systems. It is first shown that in parameter estimation techniques that do not take the measurement errors explicitly into account, like regression approaches, noisy measurements can produce inaccurate parameter estimates. Another problem is that for chaotic systems the cost functions that have to be minimized to estimate states and parameters are so complex that common optimization routines may fail. We show that the inclusion of information about the time-continuous nature of the underlying trajectories can improve parameter estimation considerably. Two approaches, which take into account both the errors-in-variables problem and the problem of complex cost functions, are described in detail: shooting approaches and recursive estimation techniques. Both are demonstrated on numerical examples.

Rank minimization and applications in system theory

Abstract: In this tutorial paper, we consider the problem of minimizing the rank of a matrix over a convex set. The rank minimization problem (RMP) arises in diverse areas such as control, system identification, statistics and signal processing, and is known to be computationally NP-hard. We give an overview of the problem, its interpretations, applications, and solution methods. In particular, we focus on how convex optimization can be used to develop heuristic methods for this problem.

A Bayesian approach to identification of hybrid systems

Abstract: In this paper, we present a novel procedure for the identification of hybrid systems in the class of piecewise ARX systems. The presented method facilitates the use of available a priori knowledge on the system to be identified, but can also be used as a black-box method. We treat the unknown parameters as random variables, described by their probability density functions. The identification problem is posed as the problem of computing the a posteriori probability density function of the model parameters, and subsequently relaxed until a practically implementable method is obtained. A particle filtering method is used for a numerical implementation of the proposed procedure. A modified version of the multicategory robust linear programming classification procedure, which uses the information derived in the previous steps of the identification algorithm, is used for estimating the partition of the piecewise ARX map. The proposed procedure is applied for the identification of a component placement process in pick-and-place machines.

Least costly identification experiement for control

Abstract: All approaches to optimal experiment design for control have so far focused on deriving an input signal (or input signal spectrum) that minimizes some control-oriented measure of plant/model mismatch between the nominal closed-loop system and the actual closed-loop system, typically under a constraint on the total input power. In practical terms, this amounts to finding the (constrained) input signal that minimizes a measure of a control-oriented model uncertainty set. Here we address the experiment design problem from a "dual" point of view and in a closed-loop setting: given a maximum allowable control-oriented model uncertainty measure compatible with our robust control specifications, what is the cheapest identification experiment that will give us an uncertainty set that is within the required bounds? The identification cost can be measured by either the experiment time, the performance degradation during experimentation due to the added excitation signal, or a combination of both. Our results are presented for the situation where the control objective is disturbance rejection only.

Convergence of the iterative Hammerstein system identification algorithm

Abstract: The convergence of the iterative identification algorithm for the Hammerstein system has been an open problem for a long time. In this paper, a detailed study is carried out and various convergence properties of the iterative algorithm are derived. It is shown that the iterative algorithm with normalization is convergent in general. Moreover, it is shown that convergence takes place in one step (two least squares iterations) for finite-impulse response Hammerstein models with i.i.d. inputs.

Identification of Support Vector Machines for Runoff Modelling

Abstract: This paper describes an exploration in using SVM (Support Vector Machine) models, which were initially developed in the Machine Learning community, in flood forecasting, with the focus on the identification of a suitable model structure and its relevant parameters for rainfall runoff modelling. SVM has been applied in many fields and has a high success rate in classification tasks such as pattern recognition, OCR, etc. The applications of SVM in regression of time series are relatively new and they are more problematic in comparison with classifications. This study found that exhaustive search of an optimum model structure and its parameter space is prohibitive due to their sheer size and unknown characteristics. Some parameters are very sensitive and can increase the CPU load tremendously (and hence result in very long computation times). All these make it very difficult to efficiently identify SVM models, which has been carried out by manual operations in all study cases so far. The paper further explored the relationships among various model structures (ξ-SV or ν-SV regression), kernel functions (linear, polynomial, radial basis and sigmoid), scaling factor, model parameters (cost C, epsilon) and composition of input vectors. These relationships should be able to provide useful information for more effective model identification in the future. The unit response curve from SVM was compared with a transfer function model and it is found that a TF model outperforms SVM in short-range predictions. It is still unclear how the unit response curve could be utilised for model identification processes and future exploration in this area is needed.

A Nonlinear Ship Manoeuvering Model: Identification and adaptive control with experiments for a model ship

Abstract: Complete nonlinear dynamic manoeuvering models of ships, with numerical values, are hard to find in the literature. This paper presents a modeling, identification, and control design where the objective is to manoeuver a ship along desired paths at different velocities. Material from a variety of references have been used to describe the ship model, its difficulties, limitations, and possible simplifications for the purpose of automatic control design. The numerical values of the parameters in the model is identified in towing tests and adaptive manoeuvering experiments for a small ship in a marine control laboratory.

Relative transfer function identification using speech signals

Abstract: An important component of a multichannel hands-free communication system is the identification of the relative transfer function between sensors in response to a desired source signal. In this paper, a robust system identification approach adapted to speech signals is proposed. A weighted least-squares optimization criterion is introduced, which considers the uncertainty of the desired signal presence in the observed signals. An asymptotically unbiased estimate for the system's transfer function is derived, and a corresponding recursive online implementation is presented. We show that compared to a competing nonstationarity-based method, a smaller error variance is achieved and generally shorter observation intervals are required. Furthermore, in the case of a time-varying system, faster convergence and higher reliability of the system identification are obtained by using the proposed method than by using the nonstationarity-based method. Evaluation of the proposed system identification approach is performed under various noise conditions, including simulated stationary and nonstationary white Gaussian noise, and car interior noise in real pseudo-stationary and nonstationary environments. The experimental results confirm the advantages of proposed approach.

Wiener model identification and predictive control of a pH neutralisation process

Abstract: Wiener model identification and predictive control of a pH neutralisation process is presented. Input-output data from a nonlinear, first principles simulation model of the pH neutralisation process are used for subspace-based identification of a black-box Wiener-type model. The proposed nonlinear subspace identification method has the advantage of delivering a Wiener model in a format which is suitable for its use in a standard linear-model-based predictive control scheme. The identified Wiener model is used as the internal model in a model predictive controller (MPC) which is used to control the nonlinear white-box simulation model. To account for the unmeasurable disturbance, a nonlinear observer is proposed. The performance of the Wiener model predictive control (WMPC) is compared with that of a linear MPC, and with a more traditional feedback control, namely a PID control. Simulation results show that the WMPC outperforms the linear MPC and the PID controllers.

Support vector method for robust ARMA system identification

Abstract: This paper presents a new approach to auto-regressive and moving average (ARMA) modeling based on the support vector method (SVM) for identification applications. A statistical analysis of the characteristics of the proposed method is carried out. An analytical relationship between residuals and SVM-ARMA coefficients allows the linking of the fundamentals of SVM with several classical system identification methods. Additionally, the effect of outliers can be cancelled. Application examples show the performance of SVM-ARMA algorithm when it is compared with other system identification methods.

On the parameter estimation and modeling of aggregate power system loads

Abstract: This paper addressed some theoretical and practical issues relevant to the problem of power system load modeling and identification. Two identification techniques are developed in the theoretical framework of stochastic system identification. The identification techniques presented in this paper belong to the family of output error models; both techniques are based on well-established equations describing load recovery mechanisms having a commonly recognized physical appeal. Numerical experiments with artificially created data were first performed on the proposed techniques and the estimates obtained proved to be asymptotically unbiased and achieved the corresponding Crame/spl acute/r-Rao lower bound. The proposed techniques were then tested using actual field measurements taken at a paper mill, and the corresponding results were used to validate a commonly used aggregate load model. The results reported in this paper indicate that the existing load models satisfactorily describe the actual behavior of the physical load and can be reliably estimated using the identification techniques presented herein.

On-line identification of non-linear hysteretic structures using an adaptive tracking technique

Abstract: System identification and damage detection based on vibration data have received considerable attention recently because of their importance to structural health monitoring. Various technical approaches have been proposed in the literature; however, the on-line identification of the changes of parameters for non-linear structures due to damages is still a challenging problem. In this paper, we propose an on-line adaptive tracking technique, based on the least-square estimation, to identify the system parameters and their changes of non-linear hysteretic structures. The method proposed is capable of tracking abrupt or slow changes of the system parameters from which the damage event and the severity of the structural damage can be detected and evaluated. Simulation results for tracking the parametric changes of non-linear hysteretic structures are presented to demonstrate the application and effectiveness of the proposed technique in detecting the structural damages.

Bounded error identification of systems with time-varying parameters

Abstract: This paper presents a new approach to guaranteed system identification for time-varying parameterized discrete-time systems. A bounded description of noise in the measurement is considered. The main result is an algorithm to compute a set that contains the parameters consistent with the measured output and the given bound of the noise. This set is represented by a zonotope, that is, an affine map of a unitary hypercube. A recursive procedure minimizes the size of the zonotope with each noise corrupted measurement. The zonotope allows us to take into account the time-varying nature of the parameters in a non conservative way. An example has been provided to clarify the algorithm.

A nonlinear least-squares approach for identification of the induction motor parameters

Abstract: A nonlinear least-squares method is presented for the identification of the induction motor parameters. A major difficulty with the induction motor is that the rotor state variables are not available measurements so that the system identification model cannot be made linear in the parameters without overparametrizing the model. Previous work in the literature has avoided this issue by making simplifying assumptions such as a "slowly varying speed." Here, no such simplifying assumptions are made. The problem is formulated as a nonlinear least-squares identification problem and uses elimination theory (resultants) to compute the parameter vector that minimizes the residual error. The only requirement is that the system must be sufficiently excited. The method is suitable for online operation to continuously update the parameter values. Experimental results are presented.

A system identification approach for video-based face recognition

Abstract: The paper poses video-to-video face recognition as a dynamical system identification and classification problem. We model a moving face as a linear dynamical system whose appearance changes with pose. An autoregressive and moving average (ARMA) model is used to represent such a system. The choice of ARMA model is based on its ability to take care of the change in appearance while modeling the dynamics of pose, expression etc. Recognition is performed using the concept of sub space angles to compute distances between probe and gallery video sequences. The results obtained are very promising given the extent of pose, expression and illumination variation in the video data used for experiments.