Subspace Identification Research Articles

A machine learning-based stochastic subspace approach for operational modal analysis of civil structures

Based on two machine learning algorithms and eight evaluation indexes, this paper proposes a novel stochastic subspace identification (SSI) approach for the operational modal analysis of civil structures. The detailed procedure of the proposed approach is first demonstrated via a numerical example of a five-degree-of-freedom (5DOF) simulation model, and the results show that the proposed approach can automatedly and effectively distinguish the physical modes from non-physical ones for the SSI. The modal parameters of the 5DOF model estimated by the proposed approach agree well with their theoretical values, verifying the accuracy and effectiveness of the proposed approach. Furthermore, the proposed approach is applied to field measurements on a 195-m-tall building under its operating condition, and the modal parameters of the building are well identified in an automated manner. Through the statistical analysis, the probability distributions and amplitude-dependent features of the natural frequencies and damping ratios of the 195-m-tall building are further revealed. The objective of this study is to provide an efficient tool for the operational modal analysis of civil structures.

The Accuracy and Computational Efficiency of the Loewner Framework for the System Identification of Mechanical Systems

The Loewner framework has recently been proposed for the system identification of mechanical systems, mitigating the limitations of current frequency domain fitting processes for the extraction of modal parameters. In this work, the Loewner framework computational performance, in terms of the elapsed time till identification, is assessed. This is investigated on a hybrid, numerical and experimental dataset against two well-established system identification methods (least-squares complex exponential, LSCE, and subspace state space system identification, N4SID). Good results are achieved, in terms of better accuracy than LSCE and better computational performance than N4SID.

Automatic modal identification via eigensystem realization algorithm with improved stabilization diagram technique

Efficient and automatic identification of modal parameters becomes increasingly important for real-time structural health monitoring (SHM) of civil structures. As spurious modes usually exist as a key problem for most output-based identification methods, great efforts have been made to eliminate them typically via stabilization-diagram techniques. However, the quality of traditional stabilization diagrams depends on preset parameters whose values usually vary from one case to another, which makes the method to be less objective and low efficient. This article proposes an improved stabilization-diagram technique, through combined usage of Monte-Carlo sampling simulation, as well as fuzzy C-means (FCM) clustering and three-stage sifting manipulations. While the Monte-Carlo simulation aims to generate more robust stable-axis, the sifting and clustering manipulations can further remove outliers and discriminate true modal results. The improved stabilization-diagram technique is then applied to two mainstream modal identification methods, i.e., eigensystem realization algorithm (ERA) and stochastic subspace identification (SSI) under the context of both a simulation study on a dynamic system and a field research about a super-tall building. Results through comparison demonstrate that the improved stabilization-diagram technique can facilitate ERA and SSI to identify modal parameters automatically and effectively at a comparably good accuracy. However, ERA outperforms SSI evidently in terms of computational efficiency (upmost 15 times faster), which is attractive for real-time SHM. Parametric analysis has been also conducted to examine detailed performance of ERA aided by the proposed stabilization-diagram technique. Overall, the aforementioned method can be adopted to achieve a good balance between identification effectiveness and computational efficiency in an automatic working pattern, and has application prospect for real-time SHM of civil structures.

A novel dynamic model parameter updating methodology of a sluice based on vibration response

Accurate dynamic model of the sluice plays an important role in the structural health monitoring and performance evaluation. It is difficult for the established model to truly and comprehensively reflect the overall mechanical characteristics of the sluice because of parameter uncertainty. Structural dynamic model updating based on vibration response is a feasible approach, but it relies on the modal parameters identification and reliable surrogate model. Therefore, a novel dynamic model parameter updating methodology of a sluice is proposed. Firstly, an improved stochastic subspace identification method based on adaptive variational mode decomposition is proposed to accurately obtain sluice modal parameters. Secondly, Kriging surrogate model based on orthogonal test method and particle swarm optimization is introduced. The mathematical surrogate model reflecting the strong non-linear relationship between modal parameters and material parameters with high sensitivity is constructed. Finally, taking the minimum relative error between the calculated and identified values of the sluice modal parameters as the objective function, whale optimization algorithm is used to optimize and the dynamic model parameter of the sluice is updated. A case of sluice physical model shows that the proposed method is feasible and reliable, which lays a great foundation for the structural health diagnosis of sluices.

Reconstruction methods for the mechanical energy of a tree under free vibration

This study examines the mechanical energy comprising the sum of kinetic energy and potential energy for improving understanding of tree dynamics under free vibration. Two methods are proposed to reconstruct the mechanical energy by means of trees’ motion and dynamic properties measured by a multi-beam flash light detection and ranging (LiDAR) sensor. The first method reconstructs the mechanical energy using the dynamic properties extracted from stochastic subspace identification. The second method uses a model updating technique that optimizes a finite-element model by minimizing an objective function, which quantifies the differences between the results obtained from the finite-element model and that measured by the LiDAR sensor, via a particle swarm optimization algorithm. The proposed methods are applied to analyze the vibration of a Ficus microcarpa under pull-and-release tests. In general, both methods yield consistent results in reconstructing the mechanical energy, kinetic energy, and potential energy of the whole tree. Results reveal that the tree tends to use more vibration modes at the beginning than at the end of vibration. The energy distribution among branches and trunk is further analyzed. The results show that the kinetic energy of the branches could exceed that of the trunk. In addition, the rate of energy dissipation is positively related to the velocity at the pulling location, and hence, the tree tends to dissipate more mechanical energy at the beginning than at the end of free vibration.

Enhancing Nonlinear Subspace Identification Using Sparse Bayesian Learning with Spike and Slab Priors

Enhancing Nonlinear Subspace Identification Using Sparse Bayesian Learning with Spike and Slab Priors

Data-driven modeling and stability control for industrial zinc roaster and its edge controller implementation

As large-scale industrial equipment, the operation stability control of the zinc roaster can improve the roasting efficiency and ensure industrial safety. In the industrial field, the roaster temperature is generally controlled manually, but automatic control is an important way to obtain real-time, accuracy, and safety of operation performance. However, existing control methods highly depend on manual experience and knowledge, which decreases their robustness and accuracy. In addition, the complex control algorithm can hardly meet the real-time requirement on the premise of pursuing accuracy. In order to address these puzzles, a data-driven explicit model predictive control solution is proposed in this paper. Specifically, the canonical correlation analysis method is introduced to extract the key controllable variables from the complex and coupled observer variables of the industrial field roaster. Then, the subspace identification method is proposed to obtain the system model with a balance between model complexity and fitting accuracy. Finally, an explicit model predictive control is introduced to simplify the calculation process of online control and simultaneously ensure the real-time stability control of the roaster. The hardware platform deployment experiment is presented to verify the feasibility and real-time performance of the proposed control scheme.

Sparse Actuator Attack Detection and Identification: A Data-Driven Approach.

This article aims to investigate the data-driven attack detection and identification problem for cyber-physical systems under sparse actuator attacks, by developing tools from subspace identification and compressive sensing theories. First, two sparse actuator attack models (additive and multiplicative) are formulated and the definitions of I/O sequence and data models are presented. Then, the attack detector is designed by identifying the stable kernel representation of cyber-physical systems, followed by the security analysis of data-driven attack detection. Moreover, two sparse recovery-based attack identification policies are proposed, with respect to sparse additive and multiplicative actuator attack models. These attack identification policies are realized by the convex optimization methods. Furthermore, the identifiability conditions of the presented identification algorithms are analyzed to evaluate the vulnerability of cyber-physical systems. Finally, the proposed methods are verified by the simulations on a flight vehicle system.

Influence of distance between the first sensor and support in determining tension of fixed-end cable using multiple synchronized vibration measurement

Non-destructive evaluation has been developed to identify cable tension for any end-rotational stiffness condition. One of the existing methods uses multiple vibration measurements. This paper aims to study the effect of shifting the closest sensor to the support in multiple vibration measurements through numerical simulation. A cable fixed at both ends vibrates under artificial random excitation is simulated. Three cases of five synchronized signal recording arrangements are applied to the cable, where the distance from the support to the first recorder (d1) is different for each case. The distance d1 of Case 1, Case 2, and Case 3 are d, 2d, and 3d, respectively, where d is the distance between the recorder, and d is taken as 7% of the total length and the same for all cases. Cable dynamical properties are analyzed using a stochastic subspace identification method, and effective lengths are figured out by curve fitting. Under the same frequency range, seven effective lengths are obtained in Case 1, while eight are detected in Cases 2 and 3. Besides, it can be concluded that Case 1 generates larger errors in predicting tension compared to other cases.

Modal identification of structures with a dynamic behaviour characterised by global and local modes at close frequencies

Identification of modal parameters of a space frame structure is a complex assignment due to a large number of degrees of freedom, close natural frequencies, and different vibrating mechanisms. Research has been carried out on the modal identification of rather simple truss structures. So far, less attention has been given to complex three-dimensional truss structures. This work develops a vibration-based methodology for determining modal information of three-dimensional space truss structures. The method uses a relatively complex space truss structure for its verification. Numerical modelling of the system gives modal information about the expected vibration behaviour. The identification process involves closely spaced modes that are characterised by local and global vibration mechanisms. To distinguish between local and global vibrations of the system, modal strain energies are used as an indicator. The experimental validation, which incorporated a modal analysis employing the stochastic subspace identification method, has confirmed that considering relatively high model orders is required to identify specific mode shapes. Especially in the case of the determination of local deformation modes of space truss members, higher model orders have to be taken into account than in the modal identification of most other types of structures.

Noise effects analysis on subspace-based damage detection with neural networks

Structural health monitoring (SHM) is nowadays a significant and topical issue in the civil engineering field, whose first-level task is the damage detection job. Recent advances in artificial intelligence (AI) combined with non-destructive assessments based on output-only vibration signals represent the frontier of SHM. The present research study has handled an AI-based multi-class damage classification task on a numerical benchmark beam problem with three different procedures. The main purpose was to investigate the noise effects of the analyzed damage detection procedures simulating real-world accelerometer sensors. The first damage identification method leverages simple statistical features of vibration signals, whereas the second method additionally considers a subspace-based damage indicator. The third method relies on a dataset composed of a specific set of damage indicators. Two deep learning (DL) techniques have been adopted to compare and verify the results, i.e. a multi-layer perceptron (MLP) and a one-dimensional convolutional network (1D-CNN). Three groups of different reasonable signal-to-noise ratio (SNR) levels were set up to simulate micro electro-mechanical system (MEMS) accelerometer sensors in real-world conditions to evaluate noise effects. In a nutshell, the results demonstrated that the DL models based on stochastic subspace identification (SSI) methods have good noise immunity performance for damage detection purposes.

Batch Process Modeling with Few-Shot Learning

Batch processes in the biopharmaceutical and chemical manufacturing industries often develop new products to meet changing market demands. When the dynamic models of these new products are trained, dynamic modeling with limited data for each product can lead to inaccurate results. One solution is to extract useful knowledge from past historical production data that can be applied to the product of a new grade. In this way, the model can be built quickly without having to wait for additional modeling data. In this study, a subspace identification combined common feature learning scheme is proposed to quickly learn a model of a new grade. The proposed modified state-space model contains common and special parameter matrices. Past batch data can be used to train common parameter matrices. Then, the parameters can be directly transferred into a new SID model for a new grade of the product. The new SID model can be quickly well trained even though there is a limited batch of data. The effectiveness of the proposed algorithm is demonstrated in a numerical example and a case of an industrial penicillin process. In these cases, the proposed common feature extraction for the SID learning framework can achieve higher performance in the multi-input and multi-output batch process regression problem.

Data-driven estimation, tracking, and system identification of deterministic and stochastic optical spot dynamics.

Stabilization, disturbance rejection, and control of optical beams and optical spots are ubiquitous problems that are crucial for the development of optical systems for ground and space telescopes, free-space optical communication terminals, precise beam steering systems, and other types of optical systems. High-performance disturbance rejection and control of optical spots require the development of disturbance estimation and data-driven Kalman filter methods. Motivated by this, we propose a unified and experimentally verified data-driven framework for optical-spot disturbance modeling and tuning of covariance matrices of Kalman filters. Our approach is based on covariance estimation, nonlinear optimization, and subspace identification methods. Also, we use spectral factorization methods to emulate optical-spot disturbances with a desired power spectral density in an optical laboratory environment. We test the effectiveness of the proposed approaches on an experimental setup consisting of a piezo tip-tilt mirror, piezo linear actuator, and a CMOS camera.

Static and Dynamic Response Characteristics of a Full-Scale Long-Cantilever Tower under Various Loading Conditions

Long-cantilever transmission towers are drawing more and more attention in ultrahigh-voltage (UHV) transmission projects. To meet the requirements of high-voltage safety clearance, the structural characteristics of long-cantilever transmission towers are significantly different from traditional ones. Aiming to ensure the safety of long-cantilever transmission towers during service, this paper investigates their static and dynamic characteristics under various extreme loading conditions based on full-scale tests and numerical simulation. With the strain data tested in seven typical cases, the bending moments and axial forces of the main members were back-calculated and the initial imperfections were calculated based on these results. Using a stochastic subspace identification algorithm, the evolution of the modal parameters during the full-scale test was revealed. The damage position of the main members was identified according to the mode shape changes, and the dynamic collapse process was analyzed via the measured dynamic responses and recorded videos. Numerical simulation was conducted in ANSYS using the calculated initial imperfections, and the results were in good agreement with the full-scale test. The results show that torsion action was not dominant for this tower and the failure mode was still the bending failure at the tower body. The proposed imperfection quantification method makes up for the deficiency of the empirical values, and using experimental results to guide numerical simulation proves practical. The modal parameters vary greatly under different loading conditions, which can be attributed to the damage after each loading case.

A Time-Series Driven Mechanical System State Description Method and Its Application in Condition Monitoring

Nonlinear and time-varying characteristics of mechanical systems may lead to the variation of fault modes which makes it hard to be accurately evaluated. To fulfill this requirement, the authors propose a time-domain signal-driven mechanical system state description method in this research. Based on the theory of stochastic subspace identification, an abnormal evaluation model is established to investigate the performance of mechanical systems. Firstly, by constructing the projection matrix of the established Hankel matrixes from the given time series at different times, the system state matrix can be obtained. Subsequently, based on the eigenvectors of the reference state matrix, the testing samples can be decomposed. Finally, by calculating the difference between the reference and testing signal, the anomaly can be acquired, and the quantitative evaluation of the health of the mechanical system can also be realized. The proposed method is validated in bearing performance degradation, bearing fault diagnosis, and milling tool wear experiments and received positive results. The proposed method, therefore, provides a new possibility for monitoring the service performance of mechanical systems.

Low-rank approximation of Hankel matrices in denoising applications for statistical damage diagnosis of wind turbine blades

Model order selection is a fundamental task in subspace identification for estimation of modal parameters, uncertainty propagation and damage diagnosis. However, the true model order and the related low-rank structure of the dynamic system are generally unknown. In this paper, a statistical methodology to actively select the dynamic signal subspace in covariance-driven subspace identification is developed on the basis of statistical analysis of the eigenvalue condition numbers of the output covariance Hankel matrix. It is shown that the condition numbers highly sensitive to random perturbations characterize the noise subspace. The signal subspace is separated from the noise subspace by analyzing two statistical parameters associated with the condition number sensitivity, whose thresholds are user-defined. A practical algorithm to retrieve the system dynamics is designed and demonstrated on a running example of a simulated wind turbine blade benchmark. The resultant framework is then applied in the context of damage detection on a medium-size wind turbine blade. It is demonstrated that the detectability of small damage is enhanced compared to the classic approaches and robustness of damage diagnosis is increased by reducing the number of false alarms.

Fast online implementation of covariance-driven stochastic subspace identification

Fast online system identification is critical for the timeliness of downstream applications such anomaly detection, condition assessment and decision making. Although some very efficient algorithms, such as the fast Fourier transform (FFT), exist, they are unable to identify damping ratios or mode shapes. The stochastic subspace identification (SSI) method is currently a widely used system identification algorithm. However, its time-consuming operation prevents downstream applications from running online in (near) real time. This paper aims to develop a fast online implementation of covariance-driven SSI (COV-SSI). Time complexity is utilized to analyze the computational cost of COV-SSI. Two steps of COV-SSI are determined to be time-consuming and are accelerated. They are (i) the computation of the covariance matrix (accelerated through incremental aggregation in the dataflow model) and (ii) the singular value decomposition (SVD) of the Toeplitz matrix (accelerated through a fast truncated SVD approach). These strategies do not require any additional parameters; the error between the proposed method and the original COV-SSI method is negligible, but the method is significantly accelerated. Finally, some numerical examples are used to validate the speed and accuracy of the fast online strategies.

Influence of system changes on closely spaced modes of a large-scale concrete tower for the application to structural health monitoring

AbstractConcrete steel towers are increasingly being used for onshore wind turbines. The lower part consists of separated segmented concrete rings connected with dry joints. Due to slight deviations from the axisymmetric cross-section, closely spaced modes occur. Therefore, the influences of small system changes on closely spaced modes, particularly the mode shapes, should be investigated to enable reliable vibration-based monitoring. In this context, the influence of imperfections due to the waviness of the dry joints requires attention. As no acceleration measurements on concrete towers considering small system changes have been performed so far, this has not yet been investigated. Therefore, an experiment is carried out using a large-scale laboratory model of a prestressed concrete segment tower. The system modifications are introduced by changing the preload. This changes the influence of imperfections of the surfaces of the horizontal dry joints, estimated by measuring strain and displacement at the lowest joint. An increasing preload causes the first two pairs of bending modes to move closer together. This enables to study the effect of the closeness of natural frequencies on the related mode shapes based on the same structure. Thus, the known effects of increasing uncertainty of the alignment and a rotation of the mode shape in the mode subspace with closer natural frequencies can be shown experimentally. In this work, the operational modal analysis (OMA) methods Bayesian-OMA (BAYOMA) and Stochastic Subspace Identification (SSI) are used. Local imperfections can significantly affect modal parameters, so these should be considered for vibration-based monitoring.

Dynamic displacement estimation and modal analysis of long-span bridges integrating multi-GNSS and acceleration measurements

Compared with acceleration-based modal analysis, displacement can provide a more reliable and robust identification result for output-only modal analysis of long-span bridges. However, the estimated displacements from acceleration records are frequently unavailable due to unrealistic drifts. Aiming at obtaining more accurate and stable results for determining the modal parameters, this study develops a multi-rate weighted data fusion approach for estimating displacement responses in dynamic monitoring of structures based on global navigation satellite system (GNSS) and acceleration measurements. The approach initially derives the local estimations from displacement and acceleration sensors via a Kalman filter algorithm with colored measurement noise, and later uses a weighted fusion criterion of scalar linear minimum variance to fuse the results of local estimations. Then, structural modal pamameters are identified by employing data-driven stochastic subspace identification (SSI) algorithm. The proposed approach is validated in a four degree-of-freedom numerical model and then applied to a long-span bridge in engineering practice. The results illustrate that the proposed approach can reduce the error of GNSS-obtained displacement and expand recognizable frequency range by introducing dynamic displacement component from acceleration measurement.

The following article for this Special Issue was published in different Issue

International Journal of Robust and Nonlinear ControlVolume 33, Issue 7 RESEARCH ARTICLE The following article for this Special Issue was published in different Issue First published: 10 April 2023 https://doi.org/10.1002/rnc.6708AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract Cheng C, Wang Q, Nikitin Y, Liu C, Zhou Y, Chen H. A data-driven distributed fault detection scheme based on subspace identification technique for dynamic systems. Int J Robust Nonlinear Control. 2023;33(5):3107-3128. doi: 10.1002/rnc.6554 https://onlinelibrary.wiley.com/doi/10.1002/rnc.6554 Volume33, Issue7Special Issue: Emerging Robust and Data‐driven Control Methods for Uncertain Learning Systems10 May 2023 RelatedInformation