Ivan Goethals

Identification of MIMO Hammerstein models using least squares support vector machines

This paper studies a method for the identification of Hammerstein models based on least squares support vector machines (LS-SVMs). The technique allows for the determination of the memoryless static nonlinearity as well as the estimation of the model parameters of the dynamic ARX part. This is done by applying the equivalent of Bais overparameterization method for identification of Hammerstein systems in an LS-SVM context. The SISO as well as the MIMO identification cases are elaborated. The technique can lead to significant improvements with respect to classical overparameterization methods as illustrated in a number of examples. Another important advantage is that no stringent assumptions on the nature of the nonlinearity need to be imposed except for a certain degree of smoothness.

Subspace identification of Hammerstein systems using least squares support vector machines

This paper presents a method for the identification of multiple-input-multiple-output (MIMO) Hammerstein systems for the goal of prediction. The method extends the numerical algorithms for subspace state space system identification (N4SID), mainly by rewriting the oblique projection in the N4SID algorithm as a set of componentwise least squares support vector machines (LS-SVMs) regression problems. The linear model and static nonlinearities follow from a low-rank approximation of a matrix obtained from this regression problem.

Identification of positive real models in subspace identification by using regularization

In time-domain subspace methods for identifying linear-time invariant dynamical systems, the model matrices are typically estimated from least squares, based on estimated Kalman filter state sequences and the observed outputs and/or inputs. It is well known that for an infinite amount of data, this least squares estimate of the system matrices is unbiased, when the system order is correctly estimated. However, for a finite amount of data, the obtained model may not be positive real, in which case the algorithm is not able to identify a valid stochastic model. In this note, positive realness is imposed by adding a regularization term to a least squares cost function in the subspace identification algorithm. The regularization term is the trace of a matrix which involves the dynamic system matrix and the output matrix.

An adaptive input–output modeling approach for predicting the glycemia of critically ill patients

In this paper we apply system identification techniques in order to build a model suitable for the prediction of glycemia levels of critically ill patients admitted to the intensive care unit. These patients typically show increased glycemia levels, and it has been shown that glycemia control by means of insulin therapy significantly reduces morbidity and mortality. Based on a real-life dataset from 15 critically ill patients, an initial input-output model is estimated which captures the insulin effect on glycemia under different settings. To incorporate patient-specific features, an adaptive modeling strategy is also proposed in which the model is re-estimated at each time step (i.e., every hour). Both one-hour-ahead predictions and four-hours-ahead simulations are executed. The optimized adaptive modeling technique outperforms the general initial model. To avoid data selection bias, 500 permutations, in which the patients are randomly selected, are considered. The results are satisfactory both in terms of forecasting ability and in the clinical interpretation of the estimated coefficients.

Subspace intersection identification of Hammerstein-Wiener systems

In this paper, a method for the identification of Hammerstein-Wiener systems is presented. The method extends the linear subspace intersection algorithm, mainly by introducing a kernel canonical correlation analysis (KCCA) to calculate the state as the intersection of past and future. The linear model and static nonlinearities are obtained from a regression problem using componentwise Least Squares Support Vector Machines (LS-SVMs).

NARX identification of hammerstein models using least squares support vector machines

Abstract In this paper we propose a new technique for the identification of NARX Hammerstein systems. The new technique is based on the theory of Least Squares Support Vector Machines function-approximation and allows to determine the memory less static nonlinearity as well as the linear model parameters. As the technique is non-parametric by nature, no assumptions about the static nonlinearity need to be made.

ENGINE SOUND COMFORTABILITY: RELEVANT SOUND QUALITY PARAMETERS AND CLASSIFICATION

Abstract In order to be able to shorten the design cycle, automobile manufacturers are interested in modelling the human perception of engine sounds. In the first part of the paper the relevant Sound Quality parameters for the prediction of engine sound comfortability are determined. The inputs are ordered with Automatic Relevance Determination and the obtained ranking is verified on the data. In the second part, models are presented to classify and compare cars on comfortability. Least Squares Support Vector Machines (LS-SVMs) is used for the classification. The influence of selecting the relevant inputs on the model performance is illustrated.

Identifying positive real models in subspace identification by using regularization

Abstract This paper deals with the lack of positive realness of identified models that may be encountered in many stochastic subspace identification procedures. Lack of positive realness is an often neglected, but important problem. Subspace identification algorithms fail to return a valid linear model if the so-called covariance model which is obtained from an intermediate realization step in the subspace identification algorithm, is not positive real. The main contribution of this paper is to introduce a regularization approach to impose positive realness on the covariance model. It is shown that positive realness can be imposed by adding a regularization term to a least squares cost function appearing in the subspace identification procedure.

On Model Complexity Control in Identification of Hammerstein Systems

Model complexity control and regularization play a crucial role in statistical learning theory and also for problems in system identification. This text discusses the potential of the issue of regularization in identification of Hammerstein systems in the context of primal-dual kernel machines and Least Squares Support Vector Machines (LS-SVMs) and proposes an extension of the Hammerstein class to finite order Volterra series and methods resulting in structure detection.