Subspace State-space Identification Research Articles

Comparison of Subspace Identification Methods for Modal Estimation of Bladed Disks

Abstract Bladed disks are critical parts of aeronautic turbojet engines requiring numerous dynamic analysis tests to fully achieve their design process. This work presents subspace state-space identification techniques for estimation of modal parameters of bladed disks using realistic although numerically generated test case data. Indeed, modal testing of bladed disks can exhibit high modal density leading to modal estimation issues. This study focuses on subspace state-space identification framework as it is an efficient way to process vector valued time series and thus to estimate modal parameters in a context of high modal density. In order to evaluate the techniques of interest, a versatile modal model has been specifically implemented to simulate data representative of full scale rotating aeronautic fan modal tests. This model is easily adjustable allowing to evaluate the identification methods in a more or less severe estimation context. The performance of the investigated methods is discussed and compared with the prescribed parameters of the model. Moreover, different techniques to estimate the order of the associated state-space model are reviewed and tested over several simulated configurations. Finally, a method to evaluate the uncertainties over the model parameters using covariance of estimator results and pseudospectrum computation is proposed and discussed over the investigated test cases.

Modal systems identification of an eleven-span concrete motorway off-ramp bridge using various excitations

This paper addresses and evaluates the influence of different types of dynamic excitation sources on identifiability and reliability of modal parameter identification of an eleven-span, post-tensioned, curved concrete motorway off-ramp bridge. The excitation sources included ground vibration waves generated by traffic on nearby motorways, people jumping on the bridge deck, broad-band linear chirp excitation induced by two light electro-dynamic shakers, and stepped sinusoidal sweeping forcing induced by a rotating eccentric mass shaker. Experimental modal analysis, operational modal analysis (OMA) and OMA with exogenous input system identification by a subspace state-space identification algorithm were carried out to extract the modal characteristics of the bridge. Numerical frequencies and mode shapes were also calculated from a detailed shell-element bridge model with the purpose of serving for the corroboration of the experimental modal properties. Through comprehensive cross-comparisons, it was revealed that the natural frequency discrepancies across different excitation methods were small (within ±1.5% relative difference), whist the consistency of the estimated damping ratios was poorer (up to 1.4% absolute difference). Eccentric mass shaker testing enabled identification of all modes predicted by the numerical model but used very heavy equipment. On the other hand, in ambient testing about one-third of the modes were missed, including the fundamental lateral mode. Electrodynamic shaker testing proved attractive as it only missed one mode and achieved its good performance with shakers that could be moved on site with relative ease.

Multilevel input signal for multivariable state-space identification of wastewater treatment plant

The purpose of this work is to identify a linear time-invariant dynamic model of wastewater treatment plants with multilevel pseudo random signals as an excitation input. The plants naturally aim to remove suspended substances, organic material and phosphate. An activated sludge process becomes the best technology available to control the discharge of pollutants. For this purpose, state-space models that emphasize on subspace-based method such as numerical subspace state-space system identification (N4SID) and ‘robust’ N4SID besides predictive estimation models are explored. The performance of identified models perturbed by multilevel input signal is validated by variance accounted for and compared to pseudo random binary input signal. It was proved that the estimated model with multilevel input offers good predicted behavior’s as compared to two-level input signal. Benchmark simulation model (BSM1) was applied as data generator for identification procedures. Key words: Multilevel input signal, multivariable subspace state-space identification, wastewater plant.

A Comparison of Methods for Forecasting Emergency Department Visits for Respiratory Illness Using Telehealth Ontario Calls

Objectives: Anticipating increases in hospital emergency department (ED) visits for respiratory illness could help time interventions such as opening flu clinics to reduce surges in ED visits. Five different methods for estimating ED visits for respiratory illness from Telehealth Ontario calls are compared, including two non-linear modeling methods. Daily visit estimates up to 14 days in advance were made at the health unit level for all 36 Ontario health units.Methods: Telehealth calls from June 1, 2004 to March 14, 2006 were included. Estimates generated by regression, Exponentially Weighted Moving Average (EWMA), Numerical Methods for Subspace State Space Identification (N4SID), Fast Orthogonal Search (FOS), and Parallel Cascade Identification (PCI) were compared to the actual number of ED visits for respiratory illness identified from the National Ambulatory Care Reporting System (NACRS) database. Model predictor variables included Telehealth Ontario calls and upcoming holidays/weekends. Models were fit using the first 304 days of data and prediction accuracy was measured over the remaining 348 days.Results: Forecast accuracy was significantly better (p<0.0001) for the 12 Ontario health units with a population over 400,000 (75% of the Ontario population) than for smaller health units. Compared to regression, FOS produced better estimates (p=0.03) while there was no significant improvement for PCI-based estimates. FOS, PCI, EWMA and N4SID performed worse than regression over the remaining smaller health units.Conclusion: Telehealth can be used to estimate ED visits for respiratory illness at the health unit level. Non-linear modeling methods produced better estimates than regression in larger health units.

Identification of Lifted Models for General Dual-Rate Sampled-Data Systems Using N4SID Algorithm

The technological and the economical reasons often make the researchers and engineers encounter the so-called multirate sampled-data systems which include multiple sampleddata mechanisms with different sampling periods. As a class of multi-rate systems, general dual-rate systems are very attractive because the contributions in the literature of the dual-rate systems can be easily extended to the whole scope of multi-rate sampled system. In this research, we consider the identification problems for the general dual-rate systems. A general dual-rate system is illustrate Fig. 1. In Fig. 1, u(kT1) and y(kT2) are the dual-rate system input and output signals and the sampling period T1 = T2. y(kT2) is corrupted by a stochastic noise v(kT2). The measurement of the output is denoted by z(kT2) . ZOH is a zero order holder with period T1. ADC is a sampler with period T2. Pc is a linear time-invariant(LTI) continuous-time process. Suppose that the samplers and zero order holders are synchronized at time t = 0. Most typical identification algorithms only handle the identification problems of single-rate systems. However, a single-rate LTI isomorphism can be obtained for the dualrate system in Fig.1 by the lifting technique. The isomorhpism is the so-called lifted model, Although there are several contributions in the literature for the identification problems of the lifted models, most of them need detailed prior information about the dual-rate system, e.g. observability structure indexes which cannot be obtained in many cases. In contrast, Subspace State-Space IDentification(4SID) algorithms need no prior information about the systems under investigation. Unfortunately, it is commented that the 4SID type algorithm cannot be used to the lifted models because of the causality constraints.

Adopting Supervisor for Bolt Loosening Detection by Using Smart Washer

The objective of this study is the loosening detection of bolted joints without human involvement by applying the concept of structural health monitoring. The smart washer consists of a cantilevered plate bonded to a piezoelectric material, which provides self-sensing and actuation functions. The basic principle of how to detect bolt loosening is that the dynamics of a smart washer system vary depending on bolt tightening axial tension. The natural frequency of the smart washer was identified by using the sub-space state space identification algorithm in previous papers. However, the previous method has the problems that the fault detection accuracy deteriorates due to the influence of identification error and modeling error. This paper propose to apply the supervisor based on the model-based Fault Detection and Isolation technique for the detection of bolt loosening by using multiple observer. The numerical simulations and the experimentations were performed to verify the possibility of the observer-based loosening detection by using the smart washer. Improvement of bolt loosening detection accuracy was confirmed by comparing the proposed method with the previous method.

116 スマートワッシャによる緩み検知に対するスーパーバイザ手法の適用(セッション4 評価・診断IV)

The objective of this study is the loosening detection of bolted joints without human involvement by applying the concept of structural health monitoring. The smart washer consists of the cantilever available to detect bolt loosening by using flexibility of cantilever and self-sensing/actuation function. The principle of how to detect the loosening of a bolt is the basis that the natural frequency of a smart washer system vary depending on a bolt tightening axial tension. The natural frequency of the smart washer was identified by using 4SID in previous papers. The natural frequency of the smart washer was identified by using the sub-space state space identification method in previous papers. However, 4SID was confirmed unsuitable for the periodic maintenance. This paper is proposed that the smart washer is detected bolt loosening by the supervisory method by using multiple observer. Numerical simulation results for several bolt loosening state for the bolted joint indicate the effectiveness of the proposed loosening detection method.

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.

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.

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.

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.

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.