Subspace System Identification Algorithm Research Articles

System identification based structural damage aggravation detection in a large masonry building

System identification is widely used to estimate the dynamic characteristics of structures using either nonparametric or parametric approaches. Parametric system identification constructs mathematical models to estimate dynamic characteristics such as natural frequency, damping ratio, and mode shapes. Also, the same approach can be used to characterize damage if periodic measurements are available. In this paper, we report damage aggravation in a large neoclassical masonry structure using system identification. We took measurements in 2019 and 2023 in the Institute of Engineering, Dean Office building, which was damaged by the 2015 Gorkha, Nepal earthquake. The building is a neoclassical three storied construction with a central courtyard and an extension along the N-S direction. Without major interventions and strengthening, the building is still in use. Using the numerical algorithms for subspace state space system identification (N4SID), vibration frequencies of the structure are identified for both measurements. Also, mode shapes are identified, and damage aggravation is detected using natural frequency and MAC parameters. The first mode frequency along the N-S direction is reduced by 44% and that along the E-W direction is reduced by 1.15%, which indicates a major damage aggravation along the N-S (Y) direction.

Supercapacitor Modeling: A System Identification Approach

Recently a great deal of attention has been given to supercapacitors (SC) due to their outstanding power densities and long cycling life. Their behavior has been extensively analyzed and tested through several modeling approaches. One common technique for modeling the dynamic operation of SCs is through an electrical circuit model (ECM). This article presents a new approach to identifying ECM parameters by applying subspace system identification (SSID) algorithms and incorporating coulombic efficiency. This novel application of SSID improves model accuracy by almost 50% in some cases compared to the literature procedures. This was done without manual tuning of the parameters, risk of non-convergence or any prior knowledge. The approach was validated at three different temperatures and with experimental data from an electric motorcycle. The resulting models are ready to be used as building blocks in a wide range of applications such as energy management systems, renewable power generation, electric vehicles, and microgrids.

Modelling of an interacting series process for rector cooling system using system identification method

This research presents the modelling of cooling system plant in the TRIGA PUSPATI reactor (RTP). The RTP cooling system involves the interacting series process which are reactor model and heat exchanger model. The behaviour process is complex due to the nonlinearity, uncertainty, and time variation of the system. Due to the nonlinearity and interacting series process of system, the numerical algorithm for subspace state space system identification (N4SID) was proposed in the modelling of RTP cooling system. However, the model was converted to the transfer function form. The output response from the simulation model of RTP cooling subsystems were analysed by comparing the model with the real operational data. The responses of the model were within the respective range of a good model data. The residual analysis for each output was also calculated. The comparison and residual analysis were done to validate the model accuracy to determine the behaviour of the model. Overall, the model accuracy assessment shows that all models are still fit in the good model region (<10%) and has a good representation of a real plant.

Novel tensor subspace system identification algorithm to identify time-varying modal parameters of bridge structures

Subspace-based system identification algorithms have been developed as an advanced technique for performing modal analysis. We introduce a novel tensor subspace-based algorithm to identify the time-varying modal parameters of bridge structures. A new time dimension is introduced in the traditional Hankel matrix, and a mathematical model of tensor subspace decomposition is established. Combined with the stabilization diagram, tensor parallel factor decomposition is used to estimate the frequencies, mode shapes, and modal damping ratios. The effectiveness of the proposed algorithm is validated by comparing it with the classical sliding-window–based stochastic subspace algorithm on a model cable-stayed bridge dynamic test. The proposed algorithm is further applied to process the dynamic responses of a real bridge health monitoring system to identify its time-varying modal frequencies. Our results demonstrated that the proposed algorithm significantly reduces computational efforts and extends the range of solution ideas for future out-only time-varying system identification problems.

Impedance Parameters Estimation of An RLCM Ladder Network Using Subspace and Similarity Transformation Approach

ABSTRACT Numerous physical systems such as transformers, sensors, and biomaterials are analysed using their equivalent ladder network model. Impedance parameters of a ladder network consist of combinations of resistances, inductances, and capacitances. Accurately determining any device impedance parameters directly from the measured time-domain input-output data is challenging. The use of non-linear optimization algorithms does not always work due to the problem being ill-conditioned. Also, the obtained parameters may not be physically realizable. In this work, the problem is approached from a black-box system identification point of view, followed by a physical parameter extraction step. The necessary current and voltage equations obtained from first principles are utilized to build a physical model in the state-space domain. With the use of a subspace system identification algorithm, the black-box parameter matrices are determined from input-output data, which do not correspond to the physical parameter matrices. However, both sets of parameters can be related through a similarity transformation matrix, leading to the extraction of the physical parameters. The novelty of the approach lies in solving the non-linear parameter estimation problem linearly without initialization. The presence of mutual inductances between various transformer winding sections makes its ladder network the most complex one. Therefore, in this paper, the ladder network model of a transformer winding is considered. As an example of the methodology, a six-section transformer ladder network is simulated and the parameter estimation results are used to validate the proposed algorithm. The same approach can be applied to estimate any other device impedance parameters.

Constrained discrete model predictive control of a greenhouse system temperature

In this paper, a constrained discete model predictive control (CDMPC) strategy for a greenhouse inside temperature is presented. To describe the dynamics of our system’s inside temperature, an experimental greenhouse prototype is engaged. For the mathematical modeling, a state space form which fits properly the acquired data of the greenhouse temperature dynamics is identified using the subspace system identification (N4sid) algorithm. The obtained model is used in order to develop the CDMPC starategy which role is to select the best control moves based on an optimization procedure under the constraints on the control notion. For efficient evaluation of the proposed control approach Matlab/Simulink and Yalmip optimization toolbox are used for algorithm and blocks implementation. The simulation results confirm the accuracy of the controller that garantees both the control and the reference tracking objectives.

Subspace identification of fault modes for a twin-rotor system

PurposeThe purpose of this paper is to identify the fault modes of a nonlinear twin-rotor system (TRS) using the subspace technique to facilitate fault identification, diagnosis and control applications.Design/methodology/approachFor identification of fault modes, three types of system malfunctions are introduced. First malfunction resembles actuator, second internal system dynamics and third represents sensor malfunction or offset. For each fault scenario, the resulting TRS model is applied with persistently exciting inputs and corresponding outputs are recorded. The collected input–output data are invoked in NS4SID subspace system identification algorithm to obtain the unknown fault model. The identified actuator fault modes of the TRS can be used for fault diagnostics, fault isolation or fault correction applications.FindingsThe identified models obtained through system identification are validated for correctness by comparing the response of the actual model under the fault condition and identified model. The results certify that the identified fault modes correctly resemble the respective fault conditions in the actual system.Originality/valueThe utilization of proposed work for current research emphasized the area of fault detection, diagnosis and correction applications that makes its value significantly. These modes when used for diagnosis purposes allow users to timely get intimated and rectify the performance degradation of the plant before it gets totally malfunctioned. Moreover, the slight performance degradation is also indicated when fault diagnosis is performed.

Stochastic subspace identification based data‐driven approach for monitoring electromechanical dynamics from phasor measurement units

This study proposes to extend the numerical algorithm for subspace state space system identification (N4SID) for power grid electromechanical dynamics monitoring using the multi-channel noisy synchrophasor measurements. The oscillation modes, mode shapes, participation factors and coherent groups are estimated in a comprehensive manner. It consists of five key steps: (i) estimation of power system state subspace model via N4SID; (ii) electromechanical modes discrimination from the trivial modes by developing the generalised inverse and mode assurance criterion; (iii) calculations of the mode shapes using the estimated states and output subspace matrices; (iv) estimation of participation factors estimated by the calculated mode shapes and (v) the generator coherency identification by developing the direction cosine denoted coherency inductor. Test results on the IEEE 16-machine 68-bus test system and the practical China Southern power Grid using field synchrophasor measurements are performed. Comparison results with other existing methods show that the proposed method achieves better accuracy and efficiency for power system electromechanical dynamics monitoring in the presence of measurement noise.

Health Monitoring of Civil Infrastructures by Subspace System Identification Method: An Overview

Structural health monitoring (SHM) is the main contributor of the future’s smart city to deal with the need for safety, lower maintenance costs, and reliable condition assessment of structures. Among the algorithms used for SHM to identify the system parameters of structures, subspace system identification (SSI) is a reliable method in the time-domain that takes advantages of using extended observability matrices. Considerable numbers of studies have specifically concentrated on practical applications of SSI in recent years. To the best of author’s knowledge, no study has been undertaken to review and investigate the application of SSI in the monitoring of civil engineering structures. This paper aims to review studies that have used the SSI algorithm for the damage identification and modal analysis of structures. The fundamental focus is on data-driven and covariance-driven SSI algorithms. In this review, we consider the subspace algorithm to resolve the problem of a real-world application for SHM. With regard to performance, a comparison between SSI and other methods is provided in order to investigate its advantages and disadvantages. The applied methods of SHM in civil engineering structures are categorized into three classes, from simple one-dimensional (1D) to very complex structures, and the detectability of the SSI for different damage scenarios are reported. Finally, the available software incorporating SSI as their system identification technique are investigated.

Development of a transient thrust stand with sub-millisecond resolution.

A transient thrust stand has been developed to offer 0.1 ms time-resolved force measurements up to 22 N. The system uses a predictor-based subspace system identification (PBSID) algorithm to obtain a high order state space model of the thrust stand. The state space model defines high-frequency vibration modes within the thrust stand. The high-frequency vibration modes are necessary to provide the time response of 0.1 ms. Thruster forces are then estimated using an augmented Kalman filter (AKF) to combine sensor traces from four accelerometers, a velocity sensor, and a displacement transducer. Fusing low-frequency displacement data with high-frequency acceleration measurements provides accurate force data from 0 kHz to 10 kHz. Combining the AKF with the PBSID state space model inherently attenuates external noise sources such as pumps. The transient thrust stand uses a torsional configuration to minimize influence from external vibrations and achieve high force resolution independent of thruster weight. Results demonstrated that the system was capable of obtaining dynamic thrust profiles with less than 5% error and a time resolution of 0.1 ms. To date, no thrust stand is capable of measuring up to 22 N forces with a time response of 10 kHz.

Subspace-Aided Closed-Loop System Identification With Application to DC Motor System

A novel closed-loop numerical algorithm for subspace state space system identification (CN4SID) is proposed in this paper. Different from standard schemes, CN4SID algorithm can extend the standard LQ decomposition to the closed-loop cases by incorporating the controller information. Moreover, the proposed method can deliver unbiased pole estimation in the closed-loop framework. To this end, CN4SID algorithm shows superior pole estimation performance compared with a class of subspace identification method via principal component analysis algorithms. The effectiveness of the proposed CN4SID algorithm is finally verified through a practical dc motor system.

Model Predictive Control Method of Simulated Moving Bed Chromatographic Separation Process Based on Subspace System Identification

Simulated moving bed (SMB) chromatographic separation is a new type of separation technology based on traditional fixed bed adsorption operation and true moving bed (TMB) chromatographic separation technology, which includes inlet‐outlet liquid, liquid circulation, and feed liquid separation. The input‐output data matrices were constructed based on SMB chromatographic separation process data. The SMB chromatographic separation process was modeled by utilizing two subspace system identification algorithms: multivariable output‐error state‐space (MOESP) identification algorithm and numerical algorithms for subspace state‐space system identification (N4SID), so as to obtain the 3rd‐order and 4th‐order state‐space yield models of the SMB chromatographic separation process, respectively. The model predictive control method based on the established state‐space models is used in the SMB chromatographic separation process. The influence of different control indicators on the predictive control system response performance is discussed. The output response curves of the yield models were obtained by changing the related parameters so that the yield model parameters are optimized set meanwhile. Finally, the simulation results showed that the yield models are successfully controlled based on the each control period and given yield range.

Active-Reactive Additional Damping Control of a Doubly-Fed Induction Generator Based on Active Disturbance Rejection Control

Large-scale wind power interfacing to the power grid has an impact on the stability of the power system. However, with an additional damping controller of the wind generator, new ways for improving system damping and suppressing the low frequency oscillation (LFO) of power systems can be put forward. In this paper, an active-reactive power additional damping controller based on active disturbance rejection control (ADRC) is proposed. In order to improve the precision of the controller, the theory of data driven control is adopted, using the numerical algorithms for subspace state space system identification (N4SID) to obtain the two order model of the ADRC controlled object. Based on the identification model, the ADRC additional damping controller is designed. Taking a 2-area 4-machine system containing the doubly fed induction generator (DFIG) wind farm as an example, it is verified that the active-reactive additional damping controller designed in this paper performs well in suppressing negative-damping LFO and forced power oscillation. When the operation state of the power system changes, it can still restrain the LFO effectively, showing stronger robustness and better effectiveness compared to the traditional proportional–integral–derivative (PID) additional damping controller.

A stochastic subspace system identification algorithm for state-space systems in the general 2-D Roesser model form

ABSTRACTThe stochastic realisation problem is associated with fitting a state-space model to a given data-set so that the second-order statistics of the output of the system match those of the data. This problem has been well studied and documented in the 1-D case, but unfortunately not so in the 2-D case, despite the similarities. Until now, the main reason behind the lack of 2-D stochastic realisation algorithms is the fact that there is a strong coupling between horizontal and vertical states, which are difficult to separate. The only known way to separate the states is to assume the model to be causal, recursive, and separable-in-denominator (CRSD). Nevertheless, there is currently no known algorithm that can solve the general 2-D stochastic realisation problem. Such problem arises naturally in image modelling, where, given an image, one needs to fit a 2-D Kalman filter model to it. In this paper, we introduce a 2-D stochastic realisation algorithm for state-space models in the general 2-D Roesser form without using the CRSD assumption. The algorithm constructs a positive real 2-D Kalman filter model. We test the algorithm with three case studies, one of which is an image example.

System identification using Nuclear Norm & Tabu Search optimization

In recent years, subspace System Identification (SI) algorithms have seen increased research, stemming from advanced minimization methods being applied to the Nuclear Norm (NN) approach in system identification. These minimization algorithms are based on hard computing methodologies. To the authors’ knowledge, as of now, there has been no work reported that utilizes soft computing algorithms to address the minimization problem within the nuclear norm SI framework. A linear, time-invariant, discrete time system is used in this work as the basic model for characterizing a dynamical system to be identified. The main objective is to extract a mathematical model from collected experimental input-output data. Hankel matrices are constructed from experimental data, and the extended observability matrix is employed to define an estimated output of the system. This estimated output and the actual – measured – output are utilized to construct a minimization problem. An embedded rank measure assures minimum state realization outcomes. Current NN-SI algorithms employ hard computing algorithms for minimization. In this work, we propose a simple Tabu Search (TS) algorithm for minimization. TS algorithm based SI is compared with the iterative Alternating Direction Method of Multipliers (ADMM) line search optimization based NN-SI. For comparison, several different benchmark system identification problems are solved by both approaches. Results show improved performance of the proposed SI-TS algorithm compared to the NN-SI ADMM algorithm.

Comparative analysis of different weight matrices in subspace system identification for structural health monitoring

Subspace System Identification (SSI) is considered as one of the most reliable tools for identification of system parameters. Performance of a SSI scheme is considerably affected by the structure of the associated identification algorithm. Weight matrix is a variable in SSI that is used to reduce the dimensionality of the state-space equation. Generally one of the weight matrices of Principle Component (PC), Unweighted Principle Component (UPC) and Canonical Variate Analysis (CVA) are used in the structure of a SSI algorithm. An increasing number of studies in the field of structural health monitoring are using SSI for damage identification. However, studies that evaluate the performance of the weight matrices particularly in association with accuracy, noise resistance, and time complexity properties are very limited. In this study, the accuracy, noise-robustness, and time-efficiency of the weight matrices are compared using different qualitative and quantitative metrics. Three evaluation metrics of pole analysis, fit values and elapsed time are used in the assessment process. A numerical model of a mass-spring-dashpot and operational data is used in this research paper. It is observed that the principal components obtained using PC algorithms are more robust against noise uncertainty and give more stable results for the pole distribution. Furthermore, higher estimation accuracy is achieved using UPC algorithm. CVA had the worst performance for pole analysis and time efficiency analysis. The superior performance of the UPC algorithm in the elapsed time is attributed to using unit weight matrices. The obtained results demonstrated that the process of reducing dimensionality in CVA and PC has not enhanced the time efficiency but yield an improved modal identification in PC.

Application of System Identification for Modeling the Dynamic Behavior of Axial Flow Compressor Dynamics

Identification of a one-stage axial compressor system is addressed. In particular, we investigate the underlying dynamics of tip air injection and throttle activation to the overall compressor dynamics and the dynamics around the tip of the compressor blades. A proposed subspace system identification algorithm is used to extract three mathematical models: relating the tip air injection to the overall dynamics of the compressor and to the flow dynamics at the tip of the compressor blade and relating the movement of the throttle to the overall compressor dynamics. As the system identification relays on experimental data, concerns about the noise level and unmodeled system dynamics are addressed by experimenting with two model structures. The identification algorithm entails a heuristic optimization that allows for inspection of the results with respect to unmodeled system dynamics. The results of the proposed system identification algorithm show that the assumed model structure for the system identification algorithm takes on an important role in defining the coupling characteristics. A new measure for the flow state in the blade passage is proposed and used in characterizing the dynamics at the tip of the compressor blade, which allows for the inspection of the limits for the utilized actuation.

Image modeling based on a 2-D stochastic subspace system identification algorithm

Fitting a causal dynamic model to an image is a fundamental problem in image processing, pattern recognition, and computer vision. In image restoration, for instance, the goal is to recover an estimate of the true image, preferably in the form of a parametric model, given an image that has been degraded by a combination of blur and additive white Gaussian noise. In texture analysis, on the other hand, a model of a particular texture image can serve as a tool for simulating texture patterns. Finally, in image enhancement one computes a model of the true image and the residuals between the image and the modeled image can be interpreted as the result of applying a de-noising filter. There are numerous other applications within the field of image processing that require a causal dynamic model. Such is the case in scene analysis, machined parts inspection, and biometric analysis, to name only a few. There are many types of causal dynamic models that have been proposed in the literature, among which the autoregressive moving average and state-space models (i.e., Kalman filter) are the most commonly used. In this paper we introduce a 2-D stochastic state-space system identification algorithm for fitting a quarter plane causal dynamic Roesser model to an image. The algorithm constructs a causal, recursive, and separable-in-denominator 2-D Kalman filter model. The algorithm is tested with three real images and the quality of the estimated images are assessed.

On-sky demonstration of optimal control for adaptive optics at Palomar Observatory.

High-order adaptive optics systems often suffer from significant computational latency, which ultimately limits the temporal error rejection bandwidth when classical controllers are employed. This Letter presents results from an on-sky, real-time implementation of an optimal controller on the PALM-3000 adaptive optics system at Palomar Observatory. The optimal controller is computed directly from open-loop wavefront measurements using a multichannel subspace system identification algorithm, and mitigates latency by explicitly predicting incident turbulence. Experimental results show a significant reduction in the residual wavefront error over the controlled spatial modes, illustrating the superior performance of the optimal control approach versus the nominal integral control architecture.

Small Signal Monitoring of Power System using Subspace System Identification

In this paper, small signal analysis of power systems is inves- tigated using Subspace System Identification (SSI) methods. Classical small signal analysis methods for power systems are based on mathematical model- ing and linearized model of power system in an especial operating point. There are some difficulties when such a classical method is applied, specially, in the case of large power systems. In this paper, such difficulties and their bases are investigated and in order to avoid them, it is suggested to use SSI algorithms for small signal analysis of power systems. The paper discusses extracting of small signal properties of power systems and presents some new suggestions for application of subspace system identification methods. Different types of subspace system identification algorithms were applied to different power sys- tem case studies using the presented propositions. The benefits and drawbacks of subspace system identification methods and the presented suggestions are studied for small signal analysis of power systems and power system monitor- ing. Several comparisons were investigated using computer simulations. The results express the usefulness and easiness of proposed methods.