| 1. |
- Bottegal, Giulio, et al.
(författare)
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Bayesian kernel-based system identification with quantized output data
- 2015
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Ingår i: IFAC-PapersOnLine. - : Elsevier. - 2405-8963. ; 48:28, s. 455-460
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we introduce a novel method for linear system identification with quantized output data. We model the impulse response as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. This serves as a starting point to cast our system identification problem into a Bayesian framework. We employ Markov Chain Monte Carlo (MCMC) methods to provide an estimate of the system. In particular, we show how to design a Gibbs sampler which quickly converges to the target distribution. Numerical simulations show a substantial improvement in the accuracy of the estimates over state-of-the-art kernel-based methods when employed in identification of systems with quantized data.
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| 2. |
- Bottegal, Giulio, et al.
(författare)
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Blind system identification using kernel-based methods
- 2015
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Ingår i: IFAC-PapersOnLine. - : Elsevier. - 2405-8963.
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Konferensbidrag (refereegranskat)abstract
- 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 Gaussian process. The structure of the covariance matrix (or kernel) of such a process is given by the stable spline kernel, which has been recently introduced for system identification purposes and depends on an unknown hyperparameter. We assume that the input can be linearly described by few parameters. We estimate these parameters, together with the kernel hyperparameter and the noise variance, using an empirical Bayes approach. The related optimization problem is efficiently solved with a novel iterative scheme based on the Expectation-Maximization (EM) method. In particular, we show that each iteration consists of a set of simple update rules. Through some numerical experiments we show that the proposed method give very promising performance.
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| 3. |
- Bottegal, Giulio, et al.
(författare)
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Modeling Complex Systems by Generalized Factor Analysis
- 2015
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Ingår i: IEEE Transactions on Automatic Control. - 0018-9286 .- 1558-2523. ; 60:3, s. 759-774
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Tidskriftsartikel (refereegranskat)abstract
- We propose a new modeling paradigm for large dimensional aggregates of stochastic systems by Generalized Factor Analysis (GFA) models. These models describe the data as the sum of a flocking plus an uncorrelated idiosyncratic component. The flocking component describes a sort of collective orderly motion which admits a much simpler mathematical description than the whole ensemble while the idiosyncratic component describes weakly correlated noise. We first discuss static GFA representations and characterize in a rigorous way the properties of the two components. The extraction of the dynamic flocking component is discussed for time-stationary linear systems and for a simple classes of separable random fields.
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| 4. |
- Bottegal, Giulio, et al.
(författare)
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Outlier robust kernel-based system identification using l1-Laplace techniques
- 2015
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Ingår i: 2015 54th IEEE Conference on Decision and Control. - : Institute of Electrical and Electronics Engineers (IEEE). ; , s. 2109-2114
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Konferensbidrag (refereegranskat)abstract
- Regularized kernel-based methods for system identification have gained popularity in recent years. However, current formulations are not robust with respect to outliers. In this paper, we study possible solutions to robustify kernel-based methods that rely on modeling noise using the Laplacian probability density function (pdf). The contribution of this paper is two-fold. First, we introduce a new outlier robust kernel-based system identification method. It exploits the representation of Laplacian pdfs as scale mixture of Gaussians. The hyperparameters characterizing the problem are chosen using a new maximum a posteriori estimator whose solution is computed using a novel iterative scheme based on the expectation-maximization method. The second contribution of the paper is the review of two other robust kernel-based methods. The three methods are compared by means of numerical experiments, which show that all of them give substantial performance improvements compared to standard kernel-based methods for linear system identification.
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| 5. |
- Ebadat, Afrooz, et al.
(författare)
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Blind identification strategies for room occupancy estimation
- 2015
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Ingår i: 2015 European Control Conference (ECC). - Piscataway, NJ : IEEE Communications Society. - 9783952426937 ; , s. 1315-1320
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Konferensbidrag (refereegranskat)abstract
- We propose and test on real data a two-tier estimation strategy for inferring occupancy levels from measurements of CO2 concentration and temperature levels. The first tier is a blind identification step, based either on a frequentist Maximum Likelihood method, implemented using non-linear optimization, or on a Bayesian marginal likelihood method, implemented using a dedicated Expectation-Maximization algorithm. The second tier resolves the ambiguity of the unknown multiplicative factor, and returns the final estimate of the occupancy levels. The overall procedure addresses some practical issues of existing occupancy estimation strategies. More specifically, first it does not require the installation of special hardware, since it uses measurements that are typically available in many buildings. Second, it does not require apriori knowledge on the physical parameters of the building, since it performs system identification steps. Third, it does not require pilot data containing measured real occupancy patterns (i.e., physically counting people for some periods, a typically expensive and time consuming step), since the identification steps are blind.
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| 6. |
- Ebadat, Afrooz, et al.
(författare)
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Multi-room occupancy estimation through adaptive gray-box models
- 2015
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Ingår i: IEEE 54th Annual Conference on Decision and Control (CDC). - Piscataway, NJ : IEEE Communications Society. - 9781479978861 ; , s. 3705-3711, s. 3705-3711
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Konferensbidrag (refereegranskat)abstract
- We consider the problem of estimating the occupancy level in buildings using indirect information such as CO2 concentrations and ventilation levels. We assume that one of the rooms is temporarily equipped with a device measuring the occupancy. Using the collected data, we identify a gray-box model whose parameters carry information about the structural characteristics of the room. Exploiting the knowledge of the same type of structural characteristics of the other rooms in the building, we adjust the gray-box model to capture the CO2 dynamics of the other rooms. Then the occupancy estimators are designed using a regularized deconvolution approach which aims at estimating the occupancy pattern that best explains the observed CO2 dynamics. We evaluate the proposed scheme through extensive simulation using a commercial software tool, IDA-ICE, for dynamic building simulation.
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| 7. |
- Ebadat, Afrooz, et al.
(författare)
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Regularized Deconvolution-Based Approaches for Estimating Room Occupancies
- 2015
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Ingår i: IEEE Transactions on Automation Science and Engineering. - : Institute of Electrical and Electronics Engineers (IEEE). - 1545-5955 .- 1558-3783. ; 12:4, s. 1157-1168
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Tidskriftsartikel (refereegranskat)abstract
- We address the problem of estimating the number of people in a room using information available in standard HVAC systems. We propose an estimation scheme based on two phases. In the first phase, we assume the availability of pilot data and identify a model for the dynamic relations occurring between occupancy levels, CO2 concentration and room temperature. In the second phase, we make use of the identified model to formulate the occupancy estimation task as a deconvolution problem. In particular, we aim at obtaining an estimated occupancy pattern by trading off between adherence to the current measurements and regularity of the pattern. To achieve this goal, we employ a special instance of the so-called fused lasso estimator, which promotes piecewise constant estimates by including an l(1) norm-dependent term in the associated cost function. We extend the proposed estimator to include different sources of information, such as actuation of the ventilation system and door opening/closing events. We also provide conditions under which the occupancy estimator provides correct estimates within a guaranteed probability. We test the estimator running experiments on a real testbed, in order to compare it with other occupancy estimation techniques and assess the value of having additional information sources.
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| 8. |
- Everitt, Niklas, et al.
(författare)
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On the Effect of Noise Correlation in Parameter Identification of SIMO Systems
- 2015
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Ingår i: IFAC-PapersOnLine. - : Elsevier. - 2405-8963. ; 48:28, s. 326-331
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Tidskriftsartikel (refereegranskat)abstract
- The accuracy of identified linear time-invariant single-input multi-output (SIMO) models can be improved when the disturbances affecting the output measurements are spatially correlated. Given a linear parametrization of the modules composing the SIMO structure, we show that the correlation structure of the noise sources and the model structure of the othe modules determine the variance of a parameter estimate. In particular we show that increasing the model order only increases the variance of other modules up to a point. We precisely characterize the variance error of the parameter estimates for finite model orders. We quantify the effect of noise correlation structure, model structure and signal spectra.
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| 9. |
- Everitt, Niklas, et al.
(författare)
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On the Variance Analysis of identified Linear MIMO Models
- 2015
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Ingår i: IEEE Explore. - : Institute of Electrical and Electronics Engineers (IEEE).
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Konferensbidrag (refereegranskat)abstract
- We study the accuracy of identified linear time-invariant multi-input multi-output (MIMO) systems. Under a stochastic framework, we quantify the effect of the spatial correlation and choice of model structure on the covariance matrix of the transfer function estimates. In particular, it is shown how the variance of a transfer function estimate depends on signal properties and model orders of other modules composing the MIMO system.
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| 10. |
- Risuleo, Riccardo Sven, 1986-, et al.
(författare)
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A benchmark for data-based office modeling: challenges related to CO2 dynamics
- 2015
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Ingår i: IFAC-PapersOnLine. - : IFAC Papers Online. - 2405-8963. ; , s. 1256-1261
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Konferensbidrag (refereegranskat)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.
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| 11. |
- Risuleo, Riccardo Sven, 1986-, et al.
(författare)
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A kernel-based approach to Hammerstein system identication
- 2015
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Ingår i: IFAC-PapersOnLine. - : IFAC Papers Online. - 2405-8963. ; , s. 1011-1016
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Konferensbidrag (refereegranskat)abstract
- n 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.
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| 12. |
- Risuleo, Riccardo Sven, 1986-, et al.
(författare)
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A new kernel-based approach to overparameterized Hammerstein system identification
- 2015
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Ingår i: 2015 54th IEEE Conference on Decision and Control (CDC). - : IEEE conference proceedings. - 9781479978847 ; , s. 115-120
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Konferensbidrag (refereegranskat)abstract
- Download CitationEmailPrintRequest PermissionsThe 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.
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| 13. |
- Risuleo, Riccardo Sven, 1986-, et al.
(författare)
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On the estimation of initial conditions in kernel-based system identification
- 2015
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Ingår i: 2015 54th IEEE Conference on Decision and Control (CDC). - : IEEE conference proceedings. - 9781479978847 ; , s. 1120-1125
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Konferensbidrag (refereegranskat)abstract
- Recent developments in system identification have brought attention to regularized kernel-based methods, where, adopting the recently introduced stable spline kernel, prior information on the unknown process is enforced. This reduces the variance of the estimates and thus makes kernel-based methods particularly attractive when few input-output data samples are available. In such cases however, the influence of the system initial conditions may have a significant impact on the output dynamics. In this paper, we specifically address this point. We propose three methods that deal with the estimation of initial conditions using different types of information. The methods consist in various mixed maximum likelihood-a posteriori estimators which estimate the initial conditions and tune the hyperparameters characterizing the stable spline kernel. To solve the related optimization problems, we resort to the expectation-maximization method, showing that the solutions can be attained by iterating among simple update steps. Numerical experiments show the advantages, in terms of accuracy in reconstructing the system impulse response, of the proposed strategies, compared to other kernel-based schemes not accounting for the effect initial conditions.
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