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Register a new userBlind Identification of ARX Models with Piecewise Constant Inputs
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Added by
Henrik Ohlsson
Publication date
2013
fields
Informatics Engineering
and research's language is
English
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Blind system identification is known to be a hard ill-posed problem and without further assumptions, no unique solution is at hand. In this contribution, we are concerned with the task of identifying an ARX model from only output measurements. Driven by the task of identifying systems that are turned on and off at unknown times, we seek a piecewise constant input and a corresponding ARX model which approximates the measured outputs. We phrase this as a rank minimization problem and present a relaxed convex formulation to approximate its solution. The proposed method was developed to model power consumption of electrical appliances and is now a part of a bigger energy disaggregation framework. Code will be made available online.
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In this paper, we present a realization and an identification algorithm for stochastic Linear Parameter-Varying State-Space Affine (LPV-SSA) representations. The proposed realization algorithm combines the deterministic LPV input output to LPV state-space realization scheme based on correlation analysis with a stochastic covariance realization algorithm. Based on this realization algorithm, a computationally efficient and statistically consistent identification algorithm is proposed to estimate the LPV model matrices, which are computed from the empirical covariance matrices of outputs, inputs and scheduling signal observations. The effectiveness of the proposed algorithm is shown via a numerical case study.
Blind system identification is known to be an ill-posed problem and without further assumptions, no unique solution is at hand. In this contribution, we are concerned with the task of identifying an ARX model from only output measurements. We phrase this as a constrained rank minimization problem and present a relaxed convex formulation to approximate its solution. To make the problem well posed we assume that the sought input lies in some known linear subspace.
This article is concerned with the identification of autoregressive with exogenous inputs (ARX) models. Most of the existing approaches like prediction error minimization and state-space framework are widely accepted and utilized for the estimation of ARX models but are known to deliver unbiased and consistent parameter estimates for a correctly supplied guess of input-output orders and delay. In this paper, we propose a novel automated framework which recovers orders, delay, output noise distribution along with parameter estimates. The primary tool utilized in the proposed framework is generalized spectral decomposition. The proposed algorithm systematically estimates all the parameters in two steps. The first step utilizes estimates of the order by examining the generalized eigenvalues, and the second step estimates the parameter from the generalized eigenvectors. Simulation studies are presented to demonstrate the efficacy of the proposed method and are observed to deliver consistent estimates even at low signal to noise ratio (SNR).
Gray-box identification is prevalent in modeling physical and networked systems. However, due to the non-convex nature of the gray-box identification problem, good initial parameter estimates are crucial for a successful application. In this paper, a new identification method is proposed by exploiting the low-rank and structured Hankel matrix of impulse response. This identification problem is recasted into a difference-of-convex programming problem, which is then solved by the sequential convex programming approach with the associated initialization obtained by nuclear-norm optimization. The presented method aims to achieve the maximum impulse-response fitting while not requiring additional (non-convex) conditions to secure non-singularity of the similarity transformation relating the given state-space matrices to the gray-box parameterized ones. This overcomes a persistent shortcoming in a number of recent contributions on this topic, and the new method can be applied for the structured state-space realization even if the involved system parameters are unidentifiable. The method can be used both for directly estimating the gray-box parameters and for providing initial parameter estimates for further iterative search in a conventional gray-box identification setup.
We propose two optimization-based heuristics for structure selection and identification of PieceWise Affine (PWA) models with exogenous inputs. The first method determines the number of affine sub-models assuming known model order of the sub-models, while the second approach estimates the model order for a given number of affine sub-models. Both approaches rely on the use of regularization-based shrinking strategies, that are exploited within a coordinate-descent algorithm. This allows us to estimate the structure of the PWA models along with its model parameters. Starting from an over-parameterized model, the key idea is to alternate between an identification step and structure refinement, based on the sparse estimates of the model parameters. The performance of the presented strategies is assessed over two benchmark examples.
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