Subspace Identification Technique Research Articles

Model Predictive Control for a Linear Parameter Varying Model of an UAV

This paper presents a Model Predictive Control (MPC) based autopilot for a fixed-wing Unmanned Aircraft Vehicle (UAV) for meteorological data sampling tasks, named Aerosonde. Aerosonde missions are featured by predetermined operating conditions, allowing the design of ad-hoc controllers for each control task by using the future knowledge of the reference signals driving the aircraft during operations. To develop the controller, the nonlinear dynamics of the vehicle has been described by a Linear Parameter-Varying (LPV) model identified from the plant data by using a subspace identification technique. The LPV model is used to design a MPC to drive the UAV. Two different Linear Parameter-Varying MPC (MPCLPV) algorithms have been proposed by introducing the previewing technique in the controller due to the a priori knowledge of full reference signals. In the design of the inner Attitude Controller (AC), a future LPV scheduling parameters estimation policy has been introduced (PF −MPCLPV) for improving the control results of the standard Previewing MPCLPV (P-MPCLPV). Furthermore, an anticipative switching approach (PS −MPCS) has been considered for the altitude External Controller (EC) to improve the control performances of the standard previewing switching MPC (P-MPCS). Both PF −MPCLPV and PS −MPCS algorithms have been compared to the P-MPCLPV and P-MPCS baseline algorithms, showing the effectiveness of proposed methods.

Multichannel deconvolution of vibrational signals: A state-space inverse filtering approach.

Deconvolution of noisy measurements, especially when they are multichannel, has always been a challenging problem. The processing techniques developed range from simple Fourier methods to more sophisticated model-based parametric methodologies based on the underlying acoustics of the problem at hand. Methods relying on multichannel mean-squared error processors (Wiener filters) have evolved over long periods from the seminal efforts in seismic processing. However, when more is known about the acoustics, then model-based state-space techniques incorporating the underlying process physics can improve the processing significantly. The problems of interest are the vibrational response of tightly coupled acoustic test objects excited by an out-of-the-ordinary transient, potentially impairing their operational performance. Employing a multiple input/multiple output structural model of the test objects under investigation enables the development of an inverse filter by applying subspace identification techniques during initial calibration measurements. Feasibility applications based on a mass transport experiment and test object calibration test demonstrate the ability of the processor to extract the excitations successfully.

Enhancing the performance of stochastic subspace identification method via energy-oriented categorization of modal components

As an advanced modal identification method, Stochastic Subspace Identification (SSI) technique has been widely used in the engineering field in recent years. However, to apply this technique properly, the characteristics of external force acting on the structural system and the data quality of response signals should meet certain requirements, which sometimes cannot be well satisfied. This may result in some problematic issues, such as mode absences. To improve the working performance of standard SSI method, this study proposes an implementation strategy which is characterized by categorization of modal components in the response into different energy groups for data preprocessing. A numerical case study is presented first, to demonstrate that a key reason for the problematic issues encountered by the standard SSI technique is the imbalanced distribution of energies associated with different modal components of the system response. The proposed method is then detailed. To implement this method, the system response should be first divided into a number of component groups with each group consisting of certain modal components, whose spectral energies are in similar order of magnitude. Then, the standard SSI technique is utilized to identify the modal parameters for each of the above component groups. Measured responses from a real super-tall building are used in the proposed method and other modal identification techniques. The results are compared to validate and evaluate the performance of the proposed method.

Subspace Identification of Linear Time-Periodic Systems With Periodic Inputs

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-revealing decomposition of the block-Hankel matrix is formulated. The consistency of the proposed method is proved under mild noise assumptions. Numerical simulation shows that the proposed method performs better than multiple widely-used time-domain subspace identification methods when an ensemble of periodic data is available.

Data-driven adaptive predictive control for an activated sludge process

Data-driven control requires no information of the mathematical model of the controlled process. This paper proposes the direct identification of controller parameters of activated sludge process. This class of data-driven control calculates the predictive controller parameters directly using subspace identification technique. By updating input-output data using receding window mechanism, the adaptive strategy can be achieved. The robustness test and stability analysis of direct adaptive model predictive control are discussed to realize the effectiveness of this adaptive control scheme. The applicability of the controller algorithm to adapt into varying kinetic parameters and operating conditions is evaluated. Simulation results show that by a proper and effective excitation of direct identification of controller parameters, the convergence and stability of the implicit predictive model can be achieved.

Analysis of Environmental and Typhoon Effects on Modal Frequencies of a Power Transmission Tower.

The structural health monitoring of power transmission towers (PTTs) has drawn increasing attention from researchers in recent years; however, no long-term monitoring of the dynamic parameters of PTTs has previously been reported in the literature. This study performed the long-term monitoring of an instrumented PTT. An automated subspace identification technique was used to extract the dynamic parameters of the PTT from ambient vibration measurements taken over approximately ten months in 2017. Ten target modal frequencies were selected to explore the effects of environmental factors, such as temperature and wind speed, as well as the root-mean-square (RMS) acceleration response of the PTT. Variations in the modal frequencies of approximately 2% to 8% were observed during the study period. In general, among the environmental factors, the temperature was found to be the primary cause of decreases in the modal frequencies, except in the case of some of the higher modes. Typhoon Nesat, which affected the PTT on July 29th, 2017, seems to have decreased the modal frequencies of the PTT, especially for the higher modes. This reduction in the modal frequencies seems to have lasted for approximately two and a half months, after which they recovered to their normal state, probably due to a seasonal cool down in temperature. The reduction percentages in the modal frequencies due to Typhoon Nesat were quantified as approximately −0.89% to −1.34% for the higher modes, but only −0.07% to −0.46% for the remaining lower modes. Although the unusual reductions in the modal frequencies are reported in this study, the reason for this phenomenon is not clear yet. Further studies would be required in the future in order to find the cause.

Data-driven fault diagnosis for dynamic traction systems in high-speed trains

Traction systems are an important aspect of high-speed trains, and their reliable operation is crucial. With data available from trains, this paper proposes an optimal fault detection and diagnosis (FDD) strategy for dynamic traction systems. Based on the established dynamic model, using sensor measurements, a correlation-aided subspace identification technique is proposed to formulate residual signals and corresponding test statistics for fault detection. Then, a modified support vector machine (SVM) is designed for optimally solving the diagnosis bias caused by the difference in the apparent probabilities of multiple fault scenarios. The feasibility and effectiveness of the proposed optical FDD performance are illustrated in the CRRC experimental platforms.

Tracking Dynamic Characteristics of Structures Using Output-Only Recursive Combined Subspace Identification Technique

AbstractIdentifying the dynamic characteristics of structures under ambient conditions is very important for heath monitoring and damage assessment. In this study, an output-only recursive combined...

Data-Driven False Data-Injection Attack Design and Detection in Cyber-Physical Systems.

In this article, a data-driven design scheme of undetectable false data-injection attacks against cyber-physical systems is proposed first, with the aid of the subspace identification technique. Then, the impacts of undetectable false data-injection attacks are evaluated by solving a constrained optimization problem, with the constraints of undetectability and energy limitation considered. Moreover, the detection of designed data-driven false data-injection attacks is investigated via the coding theory. Finally, the simulations on the model of a flight vehicle are illustrated to verify the effectiveness of the proposed methods.

State-Space Kernelized Closed-Loop Identification of Nonlinear Systems

In this paper, we propose a non-parametric state-space identification approach for open-loop and closed-loop discrete-time nonlinear systems with multiple inputs and multiple outputs. Employing a least squares support vector machine (LS-SVM) approach in a reproducing kernel Hilbert space framework, a nonlinear auto-regressive model with exogenous terms is identified to provide a non-parametric estimate of the innovation noise sequence. Subsequently, this estimate is used to obtain a compatible non-parametric estimate of the state sequence in an unknown basis using kernel canonical correlation analysis. Finally, the estimate of the state sequence is used together with the estimated innovation noise sequence to find a non-parametric state-space model, again using a LS-SVM approach. The performance of the approach is analyzed in a simulation study with a nonlinear system operating both in open loop and closed loop. The identification approach can be viewed as a nonlinear counterpart of consistent subspace identification techniques for linear time-invariant systems operating in closed loop.

Improved automated operational modal identification of structures based on clustering

A robust automated method for operational modal analysis (OMA) is in a great demand for processing a large amount of structural health monitoring data from engineering structures. This paper proposes an improved automated OMA approach based on data-driven Stochastic Subspace Identification (SSI) and clustering techniques with novel criteria. The framework of the proposed approach includes two main components, namely, “modal identification by SSI” and “automated interpretation of SSI output.” Three procedures including hard validation criteria removal, an improved statistics-based clustering procedure, and a developed cluster merging procedure are combined in the second component for automatically interpreting the stabilization diagram from the SSI output, without a priori knowledge on the modal parameters and no manual tuning during interpreting. Numerical validation results on a frame structure model demonstrate that the proposed approach is capable of identifying the vibration modes accurately, under a significant noise effect. No spurious modes are observed, and the physical modes can be accurately identified. Experimental studies on a steel frame structure in the laboratory and a real footbridge are conducted to demonstrate the robustness and applicability of using the proposed approach for automated OMA and modal tracking. Identification results are compared with baselines and those from an existing reference method to demonstrate the improvement and contribution made in the proposed approach on the automated OMA.

Multichannel processing of vibrational measurements: A constrained subspace application.

Monitoring mechanical systems operating in uncertain environments contaminated with both environmental disturbances and noise lead directly to low signal-to-noise-ratios, creating an extremely challenging processing problem, especially in real-time. In order to estimate the performance of a particular system from uncertain vibrational data, it is necessary to identify its unique resonant (modal) frequency signature. The monitoring of structural modes to determine the condition of a device under investigation is essential, especially if it is a critical entity of an operational system. The development of a model-based scheme capable of the on-line tracking of the inherent structural modal frequencies by applying both constrained subspace identification techniques to extract the modal frequencies and state estimation methods to track the evolution is discussed. An application of this approach to a cylindrical structural device (pipe-in-air) is analyzed based on theoretical simulations along with controlled validation experiments, including injected anomalies illustrate the approach and performance. Statistics are gathered to bound potential processors for real-time performance employing these constrained techniques.

Concurrent Fault Detection and Anomaly Location in Closed-Loop Dynamic Systems With Measured Disturbances

Most data-driven process monitoring approaches consider the fault detection as a binary classification issue: normal or abnormal. All deviations from the nominal operating condition can trigger the same alarms. They fail to distinguish different fluctuation patterns and locate the positions of anomalies, such as the normal deviations in operating conditions, sensors faults, actuator faults, and process faults. A new process monitoring strategy based on orthogonal decomposition (OD) is proposed for the concurrent detection and location of different deviation patterns. OD is performed to discriminate the dynamics of data driven by measured disturbances and unmeasured disturbances in the same control system. This way, the original variable space is decomposed into the deterministic subspace and stochastic subspace. A dynamic principal component analysis-based subspace identification technique is used to construct the monitoring indices in the deterministic and stochastic subspaces, respectively. Two case studies show the validity of the OD-based process monitoring approach. Note to Practitioners —Fault diagnosis based on process data models always focused on analyzing variables’ contributions to the anomaly in the past practice. But it is frequently difficult to decide the root causes just using the variables’ contributions because different faults may induce a similar variation of the same variable. This paper provides a new scheme to locate the faulty components, including the sensor faults, actuator faults, process faults, and disturbance variations. It is more pertinent to learn about the fault locations than variables’ contributions. Moreover, by locating faults first and then figuring out variables’ contributions to a specific location, more detailed and precise diagnosis conclusions can be drawn when being compared with the results of using the variables’ contributions in a global system. This new method is purely data driven and it has no demand for complex process knowledge.

Adaptive personalized multivariable artificial pancreas using plasma insulin estimates

An adaptive and personalized multivariable artificial pancreas (mAP) system using plasma insulin estimates is proposed to efficiently accommodate major disturbances to the blood glucose concentration, such as meal and physical activity. Accurate adaptive glycemic models are developed through a recursive subspace identification technique with wearable physiological measurements and estimates of unannounced meal effect and plasma insulin concentration (PIC) along with continuous glucose concentration signals to characterize the glucose concentration dynamics under various conditions such as food consumption and physical activity. The identified models with time-varying parameters are employed in the design of an adaptive model predictive control (MPC) system that is cognizant of the PIC. The adaptive controller parameters, dynamic PIC constraint, addition of physiological measurements from wearable devices, feature variables generated from the glucose measurements, and estimation of uncertain model parameters, including the meal effect, enable the mAP system to effectively compute the optimal insulin infusion over diverse diurnal variations without meal and exercise announcements. Simulation case studies using a multivariable simulator demonstrate the efficacy of the proposed mAP system.

Indirect bridge modal parameters identification with one stationary and one moving sensors and stochastic subspace identification

A new indirect strategy is proposed to estimate the bridge modal parameters from the dynamic responses of two vehicles using stochastic subspace identification technique. The effect of ambient excitation, such as ongoing traffic, is simulated as white-noise excitation at the bridge supports. The state-space model of the vehicle-bridge interaction system is derived for a single-degree-of-freedom quarter-car model and the bridge deck modeled as a simply-supported Euler-Bernoulli beam. Bridge modal frequencies can be estimated accurately from the vehicle responses. Two instrumented vehicles are required to estimate the bridge mode shapes, with one serving as a fixed reference sensor and the other as a moving sensor. The measured accelerations from the vehicles are divided into segments and each pair of signal segments forms a state-space identification problem. Local mode shape value from each signal segment can be estimated using the reference-based SSI method. A rescaling on the local mode shape values is applied to construct the global mode shapes. Effects of the bridge surface roughness, measurement noise and vehicle properties on the mode shape identification are also numerically studied. A vehicle-bridge interaction model in the laboratory serves for the experimental validation of the proposed strategy. Both numerical and experimental results show that the proposed method can estimate the bridge modal parameters with acceptable accuracy.

Free‐Decay Nonlinear System Identification via Mass‐Change Scheme

Methods for nonlinear system identification of structures generally require input‐output measured data to estimate the nonlinear model, as a consequence of the noninvariance of the FRFs in nonlinear systems. However, providing a continuous forcing input to the structure may be difficult or impracticable in some situations, while it may be much easier to only measure the output. This paper deals with the identification of nonlinear mechanical vibrations using output‐only free‐decay data. The presented method is based on the nonlinear subspace identification (NSI) technique combined with a mass‐change scheme, in order to extract both the nonlinear state‐space model and the underlying linear system. The technique is tested first on a numerical nonlinear system and subsequently on experimental measurements of a multi‐degree‐of‐freedom system comprising a localized nonlinearity.

A Unified Framework for Wavelet-Packet Identification of Dynamic Systems

This work proposes a unified framework for linear system identification in frequency subbands using wavelet packets. To that end, a previous wavelet-packet technique is extended to allow for the use of general model structures and standard identification procedures. The technique can be straightforwardly applied to the identification of models with different structures, such as subspace models, provided that their parameters can be identified using a least-squares approach. Models with autoregressive structures are used here for means of illustration. The proposed technique is illustrated with the examples of the longitudinal dynamics of a flexible aircraft and with the model of a cantilever beam. The proposed wavelet-packet approach is favorably compared with the technique on which it was based and with a recently proposed wavelet-based subspace identification technique.

Enhanced sparse component analysis for operational modal identification of real-life bridge structures

Abstract Blind source separation receives increasing attention as an alternative tool for operational modal analysis in civil applications. However, the implementations on real-life structures in literature are rare, especially in the case of using limited sensors. In this study, an enhanced version of sparse component analysis is proposed for output-only modal identification with less user involvement compared with the existing work. The method is validated on ambient and non-stationary vibration signals collected from two bridge structures with the working performance evaluated by the classic operational modal analysis methods, stochastic subspace identification and natural excitation technique combined with the eigensystem realisation algorithm (NExT/ERA). Analysis results indicate that the method is capable of providing comparative results about modal parameters as the NExT/ERA for ambient vibration data. The method is also effective in analysing non-stationary signals due to heavy truck loads or human excitations and capturing small changes in mode shapes and modal frequencies of bridges. Additionally, closely-spaced and low-energy modes can be easily identified. The proposed method indicates the potential for automatic modal identification on field test data.

Analytical investigation of railway overhead contact wire dynamics and comparison with experimental results

Abstract In this paper an analytical method for studying the free response of continuous vibrating systems with distributed and possibly non-proportional viscous damping is proposed. The most general case the method refers to is a piece-wise homogeneous Euler-Bernoulli beam, with lumped elastic and inertial elements and subjected to tensile load. The practical application of the method to a contact wire is also presented, aiming at analysing its dynamic response. Contact wires are typically used in the overhead contact line of the railway electrification system but, despite their wide diffusion, their damping properties have not been exhaustively studied. This study aims at experimentally validate the analytical method to define a reliable dynamic model of overhead contact lines. The wire is modelled as an axially loaded homogeneous beam, with lumped elastic and inertial elements (i.e. droppers and clamps). A state-form expansion applied in conjunction with a transfer matrix technique is adopted to extract the eigenvalues and to express the eigenfunctions in analytical form. Experimental measurements have been carried out in the Dynamics & Identification Research Group (DIRG) laboratory of Politecnico di Torino considering two different damping scenarios, and the modal properties of the test bench have been extracted by using a linear subspace identification technique. The damping distribution is finally investigated starting from the experimental data, in order to seek for the most appropriate damping model.

Nuclear Norm Subspace Identification Of Continuous Time State-Space Models

Subspace identification techniques derive approximate models rather than models that are optimal with respect to a goodness of fit criterion. To obtain low rank models, a nuclear norm minimization method for estimating the system matrices of linear time invariant continuous time state-space models in the presence of measurement noise is proposed. In the proposed approach, Generalized Poisson Moment Functional (GPMF) method is used to circumvent the time-derivative problem which is inherent in continuous time models. To make the proposed algorithm consistent, instrumental variables (Hankel matrix of past inputs) are considered. The accuracy of the proposed method is demonstrated with the help of numerical simulations on a variety of systems.