State-space Identification Research Articles

IDENTIFICATION OF SYNCHRONOUS GENERATORS USING “4SID” IDENTIFICATION METHOD AND NEURAL NETWOKS

Synchronous generators are multivariable systems and are well defined in a state space structure. Subspace state space (4SID) identification method is most suitable for identification of such systems. In this paper, the identification of a synchronous generator using this identification method is presented. To cover the nonlinearities, first the overall range of operation in the active (P) and reactive (Q) power plane is divided into subsections and a linear state space model is identified for the centre of each subsection. A neural network is then used to estimate the parameters for the operating conditions other than the centres of the subsections.

Bolt Loosening Detection by Using Smart Washer with 4SID and Evaluation of Temperature Characteristics

The objective of the present study is to apply the concept of structural health monitoring to the detection of loosening of a bolted joint without human involvement. This paper proposes a method of bolt loosening detection by adopting a smart washer which uses piezoelectric material with sub-space state space identification algorithm (4SID). The smart washer used in this study is in cantilever type with piezoelectric material, which adds the washer the self-sensing and actuation function. The principle used to detect the loosening of the bolts is a method of a bolt loosening detection noted that the natural frequency of a smart washer system is decreasing by the change of the bolt tightening axial tension. Therefore the study aims to identify natural frequency of a smart washer system adopting the system identification theory. The natural frequency of the smart washer was identified using sub-space state space identification method. Strong correlation was observed between the change of the natural frequency of the smart washer system and the decrement of bolt tightening axial tension. For more precise bolt loosening detection, the influence of the environmental temperature is also needed to be investigated. The experimental results indicate that the temperature change influence the bolt tightening axial tension.

A COMBINED APPROACH TO SYSTEM IDENTIFICATION OF A CLASS OF HYBRID SYSTEM

Hybrid Systems consist of continuous time and/or discrete time processes interfaced with some logical or decision making process. In this paper, a class of hybrid systems - switched linear systems is considered. It is shown that for this class of hybrid systems, it is possible to combine subspace methods with mixed integer programming. While most approaches are based on an input-output framework, we a state space identification approach is advocated. The states of the system are extracted from input-output data using sub-space methods. Once these states are known, the switched system is re-written as a mixed logical dynamical (MLD) system and the model parameters are solved for via mixed integer programming. An example is reported at the end of this paper.

Stochastic Dynamic Programming with Localized Cost-to-go Approximators: Application to Large Scale Supply Chain Management Under Demand Uncertainty

A novel optimization algorithmic framework based on dynamic programming is proposed for solving multi-product supply chain management problems with manufacturing and distribution decisions under demand uncertainty. To generate reliable suboptimal policy for simulation and restricted state space identification, a deterministic mathematical programming (MILP) approach is utilized. The simulation data with fixed action profiles obtained from the MILPs with different demand patterns is directly utilized for real-time decision making with initial ‘profit-to-go’ values.

From data to diagnosis and control using generalized orthonormal basis filters. Part I: Development of state observers

This work is aimed at the development of a state observer (steady state Kalman filter) for a multivariable system with unknown time delays, which is subjected to unmeasured disturbances. To design such a filter, we explore the feasibility of capturing system dynamics using generalized orthonormal basis filters (GOBF). A two step identification procedure is proposed by exploiting the fact that the GOBF based models have output error structure. The deterministic component of the model is identified in the first step and used to compute a residual signal. In the second step, a filter that whitens the residuals is estimated using GOBF and combined with the deterministic component. A minimal order state realization of the innovation form of the state model is then generated from this high order model using realization based sub-space based state space (4SID) identification algorithm. When time delays are not known a-priori, the similarity between GOBF and Pade approximation is used to estimates time delay matrix directly from multivariate data. The efficacy of the proposed modeling technique is demonstrated by carrying out simulation studies on the benchmark Shell control problem and experimental evaluation on a stirred tank heater (STH) system. From the analysis of simulation and experimental results, it can be inferred that the proposed approach produces fairly accurate estimates of the time delay matrix and the deterministic and stochastic components of the dynamic model.

B22 パラメータ変動モデルを利用したスマートボードの故障状態モニタリング(OS12-3 スマート構造/センシング・モニタリング)

This paper describes a modeling of a smart board composed four piezoelectric materials due to monitor and detect the fault of the system using health monitoring technique. For example, the damage of piezoelectric materials and the breaking wire. A model of the smart board with the fault is expressed by a linear parameter varying system. The output signal of the object system is affected by damage of piezoelectric materials and breaking wire. Subspace state space identification is adopted in order to detect the fault in this paper. Numerical and experimental results indicates that the fault detection can be achieved by using proposed method.

EM Algorithm for State-space Identification with Observation Outliers-An Initialization by Subspace Methods

This paper considers an improvement of estimates of a state space model obtained by subspace system identification methods via the EM algorithm in the presence of observation outliers. To initialize the EM algorithm the initial estimates are obtained by two subspace identification methods : MOESP [1] and ORT [2]. The E- and M-steps in the EM algorithm are calculated when outliers are detected, by computing the conditional expectation under the assumption that the output data is incompletely observed. The outliers are detected and deleted in the EM algorithm by a simple scheme in robust statistics by using the median of the residuals, which are defined as the difference between the observed outputs and the estimated outputs computed from the initial estimates by subspace methods. Numerical examples show that the EM algorithm can monotonically improve the initial estimates obtained by subspace identification methods.

Modal identification of bridge systems using state-space methods

Arrays of large numbers of sensors and accompanying complex system identification (SI) methods have been recently used in engineering applications on structures ranging from complex real space trusses to simple experimental beams. However, practical application to strong motion data recorded on large civil engineering systems is limited. In this study, state-space identification methods are used for modal identification from earthquake records with further investigation into the effectiveness of the methods from the viewpoint of sensor layout configuration. The study presented in this paper adopts a deterministic approach, which is complemented with statistical evaluation in another paper. The used SI methods include eigen realization, system realization with information matrix and subspace methods. The application of the methods on instrumented bridge systems in California is included and the performance of these methods is compared in terms of success and feasibility. Subsequently, viability of the methods on arrays of different numbers of sensors on the bridge systems is investigated. This is motivated by the fact that sensor arrays with wireless communication may be conveniently installed on civil engineering structures in the future. Computational costs and limits of applicability are examined using simulated ground motion analysis with detailed finite element models for a bridge system after validation using recorded data from real ground shaking. Moreover, the effect of the configuration of the sensor arrays is considered, accounting for different noise levels in the data to reflect more realistic situations. Copyright © 2005 John Wiley & Sons, Ltd.

Improved State-Space Model Identification Using Input and Output Data with Steady State Values

In this paper, we improve the deterministic off-line identification method (Kosaka et. al., 2002) that obtains a state-space model from input and output data with a constant steady state response. The method is composed of determining the parameters by zeroing the 0 ~ N-tuple integral values of output error between the plant and the model (Kosaka et. al., 2000) and by using Ho-Kalman's method (Zeiger et. al., 1974). The method theoretically has an assumption that plant system matrix A satisfies |A| < 1 because the method utilizes Taylor series expansion. But the method can be applied to plants without the assumption |A| < 1. The feature is that the method is performed by using a step response, which is suitable to a mechnical system where noise and vibration are undesirable, and that the identification result is accurate at low frequency range. Numerical simulations of multi-input multi-output system identification are illustrated.

State–Space Parameter Identification in a Second Control Laboratory

A difficulty usually encountered in the preparation of a state-space-oriented control laboratory is that most of the system identification techniques available in the literature are for input/output models. Although in recent years there has been a growing interest in state-space identification methods, the application of these techniques in undergraduate courses are not immediate since they require a deep knowledge in mathematics and system theory. In this paper, experiments are proposed to estimate the parameters of a second-order state-space system, a dc motor-generator group, whose model plays a key role in a laboratory that deals with state-space design. The efficiency of the proposed experiments is demonstrated with the estimation of all parameters of a real system.

Identification of Heffron-Phillips model parameters for synchronous generators using online measurements

The Heffron-Phillips model of a synchronous machine has successfully been used for investigating the low frequency oscillations and designing power system stabilisers. The parameters of the model are usually calculated using the synchronous generator parameters and some system variables at steady-state conditions. As the parameters of synchronous generators are not easily measurable or accurately available and steady-state calculations may have some errors, the identification of such parameters using online measurements is investigated by the authors. A generating unit is a multivariable system and is well defined in a state space structure. The sub-space state space (4SID) identification method is very suitable for the identification of such a system. This method is used to identify the parameters. Since the synchronous generators are nonlinear, the parameters of the identified Heffron-Phillips model would depend on the operating conditions. To follow such changes, a look-up table model is developed. The proposed method is first applied on a simulated nonlinear model of a synchronous generator with saturation effect and then it is applied on a micro-machine system. Simulation and experimental results show the good accuracy of the identified models.

557 ボルト緩み検知用スマートワッシャにおける諸寸法に関する実験的検証(損傷・診断, OS-17 知的材料・構造システム)

The objective was to apply a structural health monitoring concept to detect loosening of a bolt without human involvement. This paper proposes a new method of a bolt loosening detection by adopting a smart washer which uses a piezoelectric material. The proposed washer is a cantilevered plate type patched piezoelectric material. A self-sensing and actuation function featuring this material is applied to the washer. The natural frequency of the smart washer was identified with sub-space state space identification method. There was good correlation between the change of the natural frequency of the smart washer system and the decrement of bolt tightening axial tension. A result of an experiment was shown about the influence which the dimension of the smart washer and operation exert on the detection precision. A subject for the realization of loosening detection by using smart washer was mentioned.

129 パラメータ変動モデルを利用したスマート柔軟梁におけるヘルスモニタリンク

This paper describes a modeling of a smart flexible beam composed four piezoelectric materials due to detect the failure, for example, the damage of piezoelectric materials and the breaking wire. Model of the smart flexible beam in case of the failure is expressed by a linear parameter varying system. The output matrix of the object system is affected by damage of piezoelectric materials and breaking wire. Subspace state space identification is adopted in order to detect the failure. Numerical simulation indicates that the failure detection is possible by using proposed method.

753 圧電素子を用いたスマートワッシャによるボルト締結体の緩み検知

The objective was to apply a structural health monitoring concept to detect loosening of a bolt without human involvement. This paper proposes a new method of a bolt loosening detection by adopting a smart washer which uses a piezoelectric material. The proposed washer is a cantilevered plate type patched piezoelectric material. A self-sensing and actuation function featuring this material is applied to the washer. An explanation that natural frequency decreases with decrease of the bolt tightening axial tension by using the system identification, the concept of the proposed method and experiments verifying its effectiveness are described. The natural frequency of the smart washer was identified with sub-space state space identification method. There was good correlation between the change of the natural frequency of the smart washer system and the decrement of bolt tightening axial tension.

603 部分空間同定法を適用したスマートワッシャによるボルト緩み検知法

The objective was to apply a structural health monitoring concept to detect loosening of a bolt without human involvement. This paper proposes a new method of a bolt loosening detection by adopting a smart washer which uses a piezoelectric material with sub-space state spacce identification algorithm (4SID). The proposed washer is a cantilevered plate type patched piezoelectric material. A self-sensing and actuation function featuring this material is applied to the washer. An explanation that natural frequency decreases with decrease of the bolt tightening axial tension by using the system identification, the concept of the proposed method and experiments verifying its effectiveness are described. The natural frequency of the smart washer was identified with sub-space state space identification method. There was good correlation between the change of the natural frequency of the smart washer system and the decrement of bolt tightening axial tension.

201 スマートワッシャによるボルト締結体の緩み検知

The objective was to apply a structural health monitoring concept to detect loosening of a bolt without human involvement. This paper proposes a new method of a bolt loosening detection by adopting a smart washer which uses a piezoelectric material with sub-space state spacce identification algorithm (4SID). The proposed washer is a cantilevered plate type patched piezoelectric material. A self-sensing and actuation function featuring this material is applied to the washer. An explanation that natural frequency decreases with decrease of the bolt tightening axial tension by using the system identification, the concept of the proposed method and experiments verifying its effectiveness are described. The natural frequency of the smart washer was identified with sub-space state space identification method. There was good correlation between the change of the natural frequency of the smart washer system and the decrement of bolt tightening axial tension.

Identification and Control of Mechanical Systems

The control of vibrating systems is a significant issue in the design of aircraft, spacecraft, bridges and high-rise buildings. This 2001 book discusses the control of vibrating systems, integrating structural dynamics, vibration analysis, modern control and system identification. Integrating these subjects is an important feature in that engineers will need only one book, rather than several texts or courses, to solve vibration control problems. The book begins with a review of basic mathematics needed to understand subsequent material. Chapters then cover more recent and valuable developments in aerospace control and identification theory, including virtual passive control, observer and state-space identification, and data-based controller synthesis. Many practical issues and applications are addressed, with examples showing how various methods are applied to real systems. Some methods show the close integration of system identification and control theory from the state-space perspective, rather than from the traditional input-output model perspective of adaptive control. This text will be useful for advanced undergraduate and beginning graduate students in aerospace, mechanical and civil engineering, as well as for practising engineers.

System Identification and Controller Design of a Self-Sensing Piezoelectric Cantilever Structure

This paper addresses system identification and vibration control of a cantilever fabricated from piezoelectric materials, PZT, and shows how system identification and state estimation can be used to achieve self-maintenance of a self-sensing system. Currently, self-sensing systems that have concurrent actuation and sensing can be made by using a bridge circuit. However, hardware tuning is still needed due to the unstable nature of an imbalanced bridge circuit. This problem becomes serious in the space environment where human beings may not be available to perform the maintenance. A method of achieving self-sensing without a bridge circuit is proposed in this paper. Dynamics of this proposed system can be described as the state space expression with a direct transmission component. This means that the problem of balancing the bridge circuit is equivalent to the system identification and state estimation problem. By performing a simple experiment, a model of the system was identified using the 4SID, SubSpace State Space Identification method. Observer theory can be used to estimate state vectors which include information about the mechanical dynamics. Thus, system stability depends on the estimated values of the state vectors. The system can be stabilized using a state feedback controller such as a LQ controller. The proposed method was verified with experimental results, demonstrating that smart structures can achieve self-maintenance.

Estimation of the Dynamic Matrix and Noise Model for Model Predictive Control Using Closed-Loop Data

A dynamic matrix is a lower triangular matrix containing the step response coefficients of the deterministic input used in the model predictive control schemes such as the dynamic matrix controller. Subspace matrices (defined in subspace state-space identification methods) corresponding to the deterministic input and the stochastic input contain the impulse response coefficients of the deterministic and stochastic models, respectively. This paper proposes a new subspace identification based method for the estimation of the dynamic matrix of the deterministic input(s) directly from the closed-loop data. The noise model is simultaneously obtained from the closed-loop data in the impulse response form. The method is extendable to the case of measured disturbances. All of the results presented in this paper are applicable to the multivariate systems. Guidelines for the practical implementation of the algorithm are also presented in this paper. The proposed method is illustrated through MATLAB simulations and an application on a pilot-scale plant.

Further studies on temporal factor analysis: comparison and Kalman filter-based algorithm

A temporal extension of the classical factor analysis (FA) (Proceedings of the Berkeley Symposium on Mathematical Statistics and Probability, May 3, Berkeley, University of California, 1956, pp. 111–150.) has been made under the framework of temporal Bayesian Ying–Yang system (Proceedings of the International Conference on Neural Information Processing (ICONIP’98), Vol. 2, 1998, pp. 877–884; IEEE Trans. Signal Process. 48 (7) (2000) 2132 and Proceedings of the 1999 International Joint Conference on Neural Networks, Vol. 2, Washington, DC, July 1999, pp. 1071–1076). This temporal FA (TFA) not only extends the independent component analysis to Gaussian process, but also provides a new way for state-space identification without knowledge of the model parameters. In this paper, we implement the TFA algorithm provided in Xu (1998, 2000), and compare it with non-temporal one to show the importance of considering temporal relationship in factor analysis. Furthermore, we set up a connection between the TFA and traditional filtering problems in control theory, and present an alternative TFA algorithm. This new algorithm estimates the factors (also called states) and its variance by Kalman filter as an alternative to the gradient method used in that algorithm of Xu (1998, 2000), resulting in better performance in general.