State-space Identification Research Articles

DESIGNING STATE-SPACE MODELS WITH NEURAL NETWORKS

This paper presents a new state-space identification framework for non-linear systems. In particular, a state-space model structure is designed with the Group Method of Data Handling type neural network. It is assumed that the neurons of the network have tangensoidal activation functions. For such a network type, a new approach based on a bounded-error set estimation technique is employed to estimate the parameters of the network. The final part of this work contains an illustrative example regarding the application of the proposed approach in the fault detection system.

Residual models and stochastic realization in state-space identification

This paper presents theory and algorithms for validation in system identification of state-space models from finite input-output sequences in a subspace model identification framework. Our formulation includes the problem of rank-deficient residual covariance matrices, a case which is encountered in applications with mixed stochastic-deterministic input-output properties as well as for cases where outputs are linearly dependent. Similar to the case of prediction-error identification, it is shown that the resulting model can be decomposed into an input-output model and a stochastic innovations model. Using the Riccati equation, we have designed a procedure to provide a reduced-order stochastic model that is minimal with respect to system order as well as the number of stochastic inputs thereby avoiding several problems appearing in standard application of stochastic realization to the model validation problem.

A PMF-based subspace method for continuous-time model identification. Application to a multivariable winding process

This paper presents a methodology for system identification of continuous-time state-space models from finite sampled input-output signals. The estimation problem of the consecutive time-derivatives and integrals of the input-output signals is considered. The appropriate frequency characteristcs of a linear filtering based on the Poisson moment functionals in regards to the derivative or integral estimation problem is shown. The proposed method combines therefore the Poisson moment functionals technique with subspace based state-space system identification methods. The developed algorithm is based on a generalized singular value decomposition to compensate the noise colouring caused by the linear prefiltering of the input-output data. Rules of thumb are presented to choose the design parameters and new regards to the selection of the Poisson filter cut-off frequency are introduced. Finally, the proposed method is applied to a multivariable winding processes. The experimental results emphasize the applicability of the developed methodology.

A Subspace-Based Method for Continuous-Time Model Identification by Using δ-Operator Model

In this paper we derive a subspace-based state-space identification method for continuous-time systems. By using δ-operator we transform the continuous-time system to a discrete-time δ-operator state-space model which converges to the original continuous-time model as the sampling period goes to zero. Then we obtain the estimates of system matrices by applying some well-known subspace identification methods such as MOESP to the discrete-time δ-operator state-space model. We give two numerical examples to show the effectiveness of the proposed method. A beneficial comparison with the other methods such as q-, ω-and λ-operator methods is included.

Poles identification of an analog filter for nuclear spectroscopy via subspace-based techniques

In this paper, a method for the identification of the poles-zeros position of an analog amplifier for nuclear spectroscopy is presented. The proposed technique is based upon a subspace-based system state-space identification (4SID) method, which is well suited to a data set constituted by a noisy measurement of the impulse response of the circuit. The 4SID method is complemented with a preprocessing technique of the data, which improves the accuracy of the estimation. The identification method is tested both on simulated and real data sets.

Parameter extraction for microwave devices based on 4SID techniques

Microwave devices parameter extraction is achieved by a field analysis of the device, followed by a procedure which extracts lumped circuit parameters from the time domain information. The proposed algorithm is based on the 4SID (subspace-based state-space system identification) techniques, followed by an optimal order reduction.

State space identification of stable systems

This paper studies a two stage approach to state space identification with certain optimality properties. The first stage is essentially a linear correlation stage via orthonormal filtering to reduce the problem to a setup with small equivalent noise. The second stage is an optimal Hankel norm model reduction step. This two stage algorithm is shown to be consistent for a large class of stable, possibly infinite dimensional, linear time-invariant systems under a very mild condition on the additive noise. The consistency analysis is based on a non-probabilistic framework for noise which allows the inclusion of large classes of non-ergodic and non-stationary noise, possibly having deterministic components, with maximum transparency. Furthermore, l and H convergence results are derived for a popular class of ortho1 normal basis expansions based on shift operators. These bases include, e.g. Laguerre bases.

部分空間同定法の逐次化について

部分空間同定法の逐次化について

Stochastic theory of continuous-time state-space identification

This paper presents theory, algorithms, and validation results for system identification of continuous-time state-space models from finite input-output sequences. The algorithms developed are methods of subspace model identification and stochastic realization adapted to the continuous-time context. The resulting model can be decomposed into an input-output model and a stochastic innovations model. Using the Riccati equation, we have designed a procedure to provide a reduced-order stochastic model that is minimal with respect to system order as well as the number of stochastic inputs, thereby avoiding several problems appearing in standard application of stochastic realization to the model validation problem.

On Parameter Estimates in a Subspace Method for SISO Systems

A study is presented on relationships between subspace approaches and conventional parameter estimation schemes. We focus on identification of single-input-single-output(SISO) systems via the Subspace State Space Identification (4SID) method. We show that an intermediate vector which appears in the 4SID procedure is equal to the parameter of the system pulse transfer function if the model set includes the system with noise free measurements. We also show explicitly, in a elementary way, that the intermediate vector is also equivalent to the estimate via the eigenvector method in the case that the column size of the extended observability matrix is equal to ᾿(the order of the model) + 1᾿. Furthermore, we demonstrate that using a modified cost functional in the Eigenvector method corresponds to the IV-4SID method and hence gives a consistent estimate even for colored noise.

An Application of Subspace-Based Techniques to Nuclear Spectroscopy

In this paper, a method for the identification of the transfer function of an analog amplifier for nuclear spectroscopy is presented. The proposed technique is based upon a Subspace-based System State-Space Identification method, complemented with a pre-processing technique of the data, which improves the accuracy of the estimation. The identification method is tested both on simulated and real data sets.

Joint Design of Model-Subspace based State-Space Identification and Control

Recently, the importance of the joint design of identification and control has been recognized, and several controller design methods based on the iteration of identification and controller re-design have been proposed. In these methods, the frequency weighted identification plays an important role. On the other hand, as a powerful identification method, subspace state-space system identification (4SID) method has been proposed. However, it is difficult to use the frequency weight in conventional 4SID methods. In this paper, we propose a new frequency weighted subspace state-space system identification method for the joint design of identification and control. First, we give a new 4SID method using not only the input-output data of the system but also the nominal model data. Second, we show how to introduce the frequency weight to our identification method, which is relevant to the cost function for control. And third, we evaluate the effectiveness of the proposed method by a numerical example using an inverted pendulum system.

State Space Identification for a Pilot Distillation Column

Abstract The problem of black box identification of a linear MIMO model for a distillation column is considered and the N4SID subspace based algorithm for the identification of linear state space models is applied to a set of experimental data. Model order selection and experiment design are based on a simulation study, performed on a non linear model of the plant. The comparison of the response of the identified model with the response of the plant shows a very satisfactory degree of accordance.

High-accuracy fit of the poles of spectroscopy amplifiers designed for mixed analog-digital filtering

In this paper, a method for the identification of the poles' and zeros' position of an analog amplifier for nuclear spectroscopy used as a prefilter for a subsequent digital filter setup is presented. The proposed technique is based upon a subspace-based system state-space identification (4SID) method, which is well suited to a data set constituted by a noisy measurement of the sampled impulse response of the circuit. The algorithm runs unassisted and does not require skills by the operator. The experiments confirm that by using the so-obtained pole values, the shape of the impulse response of the amplifier can be fit with much better than 1% accuracy. Consequently, the overall filtering (analog+digital) can have finite duration and a top with a flatness much better than 1%.

Canonical correlation analysis, approximate covariance extension, and identification of stationary time series

In this paper we analyze a class of state space identification algorithms for time-series, based on canonical correlation analysis, in the light of recent results on stochastic systems theory. In principle, these so called “subspace methods” can be described as covariance estimation followed by stochastic realization. The methods offer the major advantage of converting the nonlinear parameter estimation phase in traditional ARMA models identification into the solution of a Riccati equation but introduce at the same time some nontrivial mathematical problems related to positivity. The reason for this is that an essential part of the problem is equivalent to the well-known rational covariance extension problem. Therefore, the usual deterministic arguments based on factorization of a Hankel matrix are not valid for generic data, something that is habitually overlooked in the literature. We demonstrate that there is no guarantee that several popular identification procedures based on the same principle will not fail to produce a positive extension, unless some rather stringent assumptions are made which, in general, are not explicitly reported. In this paper the statistical problem of stochastic modeling from estimated covariances is phrased in the geometric language of stochastic realization theory. We review the basic ideas of stochastic realization theory in the context of identification, discuss the concept of stochastic balancing and of stochastic model reduction by principal subsystem truncation. The model reduction method of Desai and Pal (1982) [A realization approach to stochastic model reduction. Proc. 1 st Decision and Control Conf., pp. 1105–1112.], based on truncated balanced stochastic realizations, is partially justified, showing that the reduced system structure has a positive covariance sequence but is in general not balanced. As a byproduct of this analysis we obtain a theorem prescribing conditions under which the ‘subspace identification’ methods produce bona fide stochastic systems.

Time Domain State Space Identification of Structural Systems

An integrated time domain state space identification technique for structural systems is presented. This technique integrates the Observability Range Space Extraction identification algorithm, Balanced Realization model reduction algorithm, and Least Square model updating algorithm to generate low order and highly accurate state space models for structural systems based upon time domain data. The algorithms are integrated in such a manner that the Observability Range Space Extraction identification algorithm is used to generate an initial overparameterized state space model and then the Balanced Realization model reduction and Least Square model updating algorithms are used to iteratively reduce and update the model to achieve minimum prediction errors in time domain. We shall present the Observability Range Space Extraction identification algorithm and the Least Square model updating algorithm and discuss the integrated identification technique. The MIT Middeck Active Control Experiment (MACE) is used as an application example. MACE is an active structure control experiment to be conducted in the Space Shuttle middeck. Results of ground experiments using this technique will be discussed.

A technique for the identification of linear periodic state-space models

A non-stochastic state-space identification algorithm for linear time-invariant systems is modified for use with periodic linear systems. Like its predecessor, the modified algorithm forms block Hankel matrices from input-output data and uses the singular value decomposition of these Hankel matrices to compute state vector sequences. The state vector sequences are then used to compute system matrices associated with the periodic linear system by solving an (overdetermined) linear system. The modifications to the original algorithm are as follows. First, the periodic system of period p is viewed as p separate time-invariant period-mapped systems. This technique allows the structure of a periodic Hankel matrix to be deduced, which in turn allows a state vector sub-sequence for the periodic system to be computed. When a complete state vector sequence is computed, it is used directly to construct the periodic state-space models. Second, similarities in the structure of each of the periodic Hankel matrices ass...

State Space Identification of Linear Deterministic Rainfall‐Runoff Models

Rainfall‐runoff models of the black box type abound in the water resources literature (i.e., transfer function, autoregressive moving average (ARMA), ARMAX, state space, etc.). The corresponding system identification algorithms for such models are known to be numerically efficient and accurate, leading in most cases to good parsimonious representations of the rainfall‐runoff process. Alternatively, every model in transfer function, ARMA, and ARMAX form has an equivalent state space representation. However, state space models do not necessarily have simple system identification algorithms, unless the system matrices are restricted to some canonical form. Furthermore, state space system identification algorithms that work with the rainfall/runoff data directly (i.e., covariance free), require initial conditions and are inherently iterative and nonlinear. In this paper we present a state space system identification theory which overcomes these limitations. One advantage of such a theory is that the corresponding algorithms are highly robust to additive noise in the data. They are referred to as “subspace algorithms” due to their ability to separate the signal subspace from the noise subspace. The main advantages of the subspace algorithms are the automatic structure identification (system order), geometrical insights (notions of angle between subspaces), and the fact that they rely on robust numerical procedures (singular value decomposition). In this paper, two algorithms are presented. The first one is a two‐step procedure, where the impulse response (unit hydrograph ordinates for the single‐input, single‐output case) are computed from the input/output data by solving a constrained deconvolution problem. These impulse response ordinates are then used as inputs for identifying the system matrices by means of a Hankel‐based realization algorithm. The second approach uses the data directly to identify the system matrices, bypassing the deconvolution step. The algorithms are tested with real data from the Voer catchment in Belgium.

Fully Parametrized State-Space Models in System Identification

In this paper we consider identification of multivariable linear systems using state-space models. A new model structure which is fully parametrized is introduced. All systems of a given order. can be described with this model structure and thus relieve us from all the internal structural issues otherwise inherent in the multivariable state-space identification problem. We present an identification algorithm which minimize a regularized prediction error criterion. We show that the proposed model structure retains the statistical properties of the standard identifiable model structures. The proposed identification algorithm is shown to locally converge to the set of true systems. Examples are given illustrating the results as well as showing the practical use of the proposed model structure using real data.

Fast identification of state-space models via exploitation of displacement structure

The computational burden of state-space model identification has prevented its real-time application, although it offers some important advantages over other methods based on input/output transfer functions. A recently proposed state-space identification method uses ideas from sensor array signal processing to somewhat reduce the computational burden. The major costs still remain because of the need for the singular value (or sometimes QR) decomposition, which requires O(MN/sup 2/) hops and O(N/sup 2/) storage when the data matrix has size M/spl times/N, N>M. It turns out that proper exploitation, using results from the theory of displacement structure, of the Toeplitz-like nature of several matrices arising in the procedure reduces the computational effort to O(MN) flops with O(M/sup 2/+N) storage. Further computational gains are made by using the recently developed fast subspace decomposition methods. Results of the study of an actual system are described. >