The identification of multivariable state space models in innovation form is solved in a subspace identification framework using convex nuclear norm optimization. The convex optimization approach allows to include constraints on the unknown matrices in the data-equation characterizing subspace identification methods, such as the lower triangular block-Toeplitz of weighting matrices constructed from the Markov parameters of the unknown observer. The classical use of instrumental variables to remove the influence of the innovation term on the data equation in subspace identification is avoided. The avoidance of the instrumental variable projection step has the potential to improve the accuracy of the estimated model predictions, especially for short data length sequences. This is illustrated using a data set from the DaSIy library. An efficient implementation in the framework of the Alternating Direction Method of Multipliers (ADMM) is presented that is used in the validation study.
In this paper, we establish a unified framework for subspace identification (SID) of linear parameter-varying (LPV) systems to estimate LPV state-space (SS) models in innovation form. This framework enables us to derive novel LPV SID schemes that are extensions of existing linear time-invariant (LTI) methods. More specifically, we derive the open-loop, closed-loop, and predictor-based data-equations, an input-output surrogate form of the SS representation, by systematically establishing an LPV subspace identification theory. We show the additional challenges of the LPV setting compared to the …
This paper proposes a new methodology for subspace identification of linear time-periodic (LTP) systems with periodic inputs. This method overcomes the issues related to the computation of frequency response of LTP systems by utilizing the frequency response of the time-lifted system with linear time-invariant structure instead. The response is estimated with an ensemble of input-output data with periodic inputs. This allows the frequency-domain subspace identification technique to be extended to LTP systems. The time-aliased periodic impulse response can then be estimated and the order-reveal…
Model estimates obtained from traditional subspace identification methods may be subject to significant variance. This elevated variance is aggravated in the cases of large models or of a limited sample size. Common solutions to reduce the effect of variance are regularized estimators, shrinkage estimators and Bayesian estimation. In the current work we investigate the latter two solutions, which have not yet been applied to subspace identification. Our experimental results show that our proposed estimators may reduce the estimation risk up to $40\%$ of that of traditional subspace methods.
The subspace method is one of the mainstream system identification method of linear systems, and its basic idea is to estimate the system parameter matrices by projecting them into a subspace related to input and output. However, most of the existing subspace methods cannot have the statistic performance guaranteed since the lack of closed-form expression of the estimation. Meanwhile, traditional subspace methods cannot deal with the uncertainty of the noise, and thus stable identification results cannot be obtained. In this paper, we propose a novel improved subspace method from the perspecti…
We present an algorithmic framework for the identification of candidate invariant subspaces for switched linear systems. Namely, the framework allows to compute an orthonormal basis in which the matrices of the system are close to block-triangular matrices, based on a finite set of observed one-step trajectories and with a priori confidence level. The link between the existence of an invariant subspace and a common block-triangularization of the system matrices is well known. Under some assumptions on the system, one can also infer the existence of an invariant subspace when the matrices are c…
Operational Modal Analysis (OMA) provides essential insights into the structural dynamics of an Offshore Wind Turbine (OWT). In these dynamics, damping is considered an especially important parameter as it governs the magnitude of the response at the natural frequencies. Violation of the stationary white noise excitation requirement of classical OMA algorithms has troubled the identification of operational OWTs due to harmonic excitation caused by rotor rotation. Recently, a novel algorithm was presented that mitigates harmonics by estimating a harmonic subsignal using a Kalman filter and orth…
Subspace identification (SID) has been widely used in system identification and control fields since it can estimate system models only relying on the input and output data by reliable numerical operations such as singular value decomposition (SVD). However, high-dimension Hankel matrices are involved to store these data and used to obtain the system models, which increases the computation amount of SID and leads SID not suitable for the large-scale or real-time identification tasks. In this paper, a novel fast SID method based on cloud workflow processing and container technology is proposed …
Eindhoven University of Technology（埃因霍温理工大学）；Institute for Computer Science and Control（计算机科学与控制研究所）
Continuous-time (CT) modeling has proven to provide improved sample efficiency and interpretability in learning the dynamical behavior of physical systems compared to discrete-time (DT) models. However, even with numerous recent developments, the CT nonlinear state-space (NL-SS) model identification problem remains to be solved in full, considering common experimental aspects such as the presence of external inputs, measurement noise, latent states, and general robustness. This paper presents a novel estimation method that addresses all these aspects and that can obtain state-of-the-art result…
In this paper, we investigate the feasibility of using subspace system identification techniques for estimating transient Structural-Thermal-Optical Performance (STOP) models of reflective optics. As a test case, we use a Newtonian telescope structure. This work is motivated by the need for the development of model-based data-driven techniques for prediction, estimation, and control of thermal effects and thermally-induced wavefront aberrations in optical systems, such as ground and space telescopes, optical instruments operating in harsh environments, optical lithography machines, and optical…
In a direct data-driven approach, this paper studies the {\em property identification(ID)} problem to analyze whether an unknown linear system has a property of interest, e.g., stabilizability and structural properties. In sharp contrast to the model-based analysis, we approach it by directly using the input and state feedback data of the unknown system. Via a new concept of sufficient richness of input sectional data, we first establish the necessary and sufficient condition for the minimum input design to excite the system for property ID. Specifically, the input sectional data is sufficient…
Stable Linear Subspace Identification: A Machine Learning Approach
Swiss Federal Laboratories for Materials Science and Technology (Empa)（瑞士联邦材料科学与技术研究所（Empa））；Swiss Federal Institute of Technology Lausanne (EPFL)（洛桑联邦理工学院（EPFL））
