Riccardo Sven Risuleo

A kernel-based approach to Hammerstein system identification

Abstract In this paper, we propose a novel algorithm for the identification of Hammerstein systems. Adopting a Bayesian approach, we model the impulse response of the unknown linear dynamic system as a realization of a zero-mean Gaussian process. The covariance matrix (or kernel) of this process is given by the recently introduced stable-spline kernel, which encodes information on the stability and regularity of the impulse response. The static nonlinearity of the model is identified using an Empirical Bayes approach, i.e. by maximizing the output marginal likelihood, which is obtained by integrating out the unknown impulse response. The related optimization problem is solved adopting a novel iterative scheme based on the Expectation-Maximization method, where each iteration consists in a simple sequence of update rules. Numerical experiments show that the proposed method compares favorably with a standard algorithm for Hammerstein system identification.

Blind system identification using kernel-based methods*

We propose a new method for blind system identification (BSI). Resorting to a Gaussian regression framework, we model the impulse response of the unknown linear system as a realization of a Gaussia ...

A new kernel-based approach to overparameterized Hammerstein system identification

The object of this paper is the identification of Hammerstein systems, which are dynamic systems consisting of a static nonlinearity and a linear time-invariant dynamic system in cascade. We assume that the nonlinear function can be described as a linear combination of p basis functions. We model the system dynamics by means of an np-dimensional vector. This vector, usually referred to as overparameterized vector, contains all the combinations between the nonlinearity coefficients and the first n samples of the impulse response of the linear block. The estimation of the overparameterized vector is performed with a new regularized kernel-based approach. To this end, we introduce a novel kernel tailored for overparameterized models, which yields estimates that can be uniquely decomposed as the combination of an impulse response and p coefficients of the static nonlinearity. As part of the work, we establish a clear connection between the proposed identification scheme and our recently developed nonparametric method based on the stable spline kernel.

A nonparametric kernel-based approach to Hammerstein system identification

Hammerstein systems are the series composition of a static nonlinear function and a linear dynamic system. In this work, we propose a nonparametric method for the identification of Hammerstein systems. We adopt a kernel-based approach to model the two components of the system. In particular, we model the nonlinear function and the impulse response of the linear block as Gaussian processes with suitable kernels. The kernels can be chosen to encode prior information about the nonlinear function and the system. Following the empirical Bayes approach, we estimate the posterior mean of the impulse response using estimates of the nonlinear function, of the hyperparameters, and of the noise variance. These estimates are found by maximizing the marginal likelihood of the data. This maximization problem is solved using an iterative scheme based on the expectation-conditional maximization, which is a variation of the standard expectation–maximization method for solving maximum-likelihood problems. We show the effectiveness of the proposed identification scheme in some simulation experiments.

A benchmark for data-based office modeling: challenges related to CO2 dynamics

Abstract This paper describes a benchmark consisting of a set of synthetic measurements relative to an office environment simulated with the software IDA-ICE. The simulated environment reproduces a laboratory at the KTH-EES Smart Building, equipped with a building management system. The data set contains measurement records collected over a period of several days. The signals correspond to CO2 concentration, mechanical ventilation airows, air infiltrations and occupancy. Information on door and window opening is also available. This benchmark is intended for testing data-based modeling techniques. The ultimate goal is the development of models to improve the forecast and control of environmental variables. Among the numerous challenges related to this framework, we focus on the problem of occupancy estimation using information on CO2 concentration, which we treat as a blind identification problem. For benchmarking purposes, we present two different identification approaches: a baseline overparameterization method and a kernel-based method.

Kernel-based system identification from noisy and incomplete input-output data

In this contribution, we propose a kernel-based method for the identification of linear systems from noisy and incomplete input-output datasets. We model the impulse response of the system as a Gaussian process whose covariance matrix is given by the recently introduced stable spline kernel. We adopt an empirical Bayes approach to estimate the posterior distribution of the impulse response given the data. The noiseless and missing data samples, together with the kernel hyperparameters, are estimated maximizing the joint marginal likelihood of the input and output measurements. To compute the marginal-likelihood maximizer, we build a solution scheme based on the Expectation-Maximization method. Simulations on a benchmark dataset show the effectiveness of the method.

Blind system identification using kernel-based methods**This work was supported by the European Research Council under the advanced grant LEARN, contract 267381 and by the Swedish Research Council under contract 621-2009-4017.

We propose a new method for blind system identification (BSI). Resorting to a Gaussian regression framework, we model the impulse response of the unknown linear system as a realization of a Gaussia ...

Blind system identification using kernel-based methods

We propose a new method for blind system identification (BSI). Resorting to a Gaussian regression framework, we model the impulse response of the unknown linear system as a realization of a Gaussia ...