Subspace Identification Research Articles

An edge-computing framework for operational modal analysis of offshore wind-turbine tower

With massive construction of offshore wind turbines (OWT), structural health monitoring (SHM) techniques have been applied to estimate the working conditions and provide early warnings of structural damage. This study proposes an edge-computing-based SHM system for operational modal analysis (OMA) of an OWT. ThssCe system comprised an open-source data acquisition (DAQ) device, a Raspberry Pi single-board computer, and associated drivers, protocols, and algorithms. The DAQ device can measure the acceleration response of an operating OWT subjected to environmental excitation and transmit raw signals to the Raspberry Pi according to the UDP protocol. The data are further processed to obtain the first-order frequency via an OMA algorithm developed by combining Kalman filtering, the random decrement technique (RDT), and the stochastic subspace identification (SSI) method. The proposed SHM system was implemented in a scaled OWT model to verify its feasibility for field use. The experimental results indicate that (1) the edge-computing-based SHM system can accurately measure the response of the OWT; (2) the proposed algorithm can estimate the modal information of the OWT during operation; (3) the variation in the first-order frequency induced by lateral loads can be identified by the SHM system. Unlike a centralized SHM system, the proposed edge-computing-based SHM system does not require massive data transmission, making it promising for offshore environments.

Development of a software platform for bridge modal and damage identification based on ambient excitation

Modal and damage identification based on ambient excitation can greatly improve the efficiency of high-speed railway bridge vibration detection. This paper first describes the basic principles of stochastic subspace identification, peak-picking, and frequency domain decomposition method in modal analysis based on ambient excitation, and the effectiveness of these three methods is verified through finite element calculation and numerical simulation. Then the damage element is added to the finite element model to simulate the crack, and the curvature mode difference and the curvature mode area difference square ratio are calculated by using the stochastic subspace identification results to verify their ability of damage identification and location. Finally, the above modal and damage identification techniques are integrated to develop a bridge modal and damage identification software platform. The final results show that all three modal identification methods can accurately identify the vibration frequency and mode shape, both damage identification methods can accurately identify and locate the damage, and the developed software platform is simple and efficient.

Battery leakage fault diagnosis based on multi-modality multi-classifier fusion decision algorithm

With the rapid development of the new energy vehicle industry and the overall number of electric vehicles, the thermal runaway problem of lithium-ion batteries has become a major obstacle to the promotion of electric vehicles. During actual usage, the battery leakage problem leads to the degradation of the system performance, which may cause arcing, external short circuit or even thermal runaway. Therefore, it is essential to analyze the internal mechanism of electrolyte leakage phenomenon and design the corresponding fault diagnosis algorithm. This work tests the disassembled leaking battery module of the practical vehicle. The incremental capacity analysis of the charging process indicated that the battery had capacity loss, and the voltage signal trend analysis of the discharging process found that the leaking battery had higher voltage difference slope. The detection results based on the electrochemical impedance spectrum (EIS) test corroborate the anomaly internal impedance of the battery. Moreover, an incremental capacity bar graph analysis method based on cloud data is designed and the ohm resistance is calculated by a simplified subspace identification algorithm. On this basis, the threshold alarm information is incorporated to form a feature matrix, and a machine learning fault diagnosis algorithm based on multi-modality multi-classifier fusion decision framework is proposed, which is capable of scoring and quantifying the hazard level of fault types such as electrolyte leakage, and achieve up to 26 days advance warning on cloud-based real-vehicle data.

Amplitude dependence of natural frequency and damping ratio for 5 supertall buildings with moderate-to-strong typhoon-induced vibrations

Modal parameters play a significant role in the wind-resistant design and vibration control of high-rise buildings. Results from previous studies demonstrate that the natural frequency and damping ratio of high-rise buildings usually exhibit nonlinear variation characteristics with the increase of structural amplitude. However, due to lacking relevant field measurements, the features of natural frequency and damping ratio for super-tall buildings under large wind-induced amplitudes have been less explored. This paper presents a field study on typhoon-induced structural responses of five supertall buildings whose structural heights all exceed 300 m. The peak acceleration responses at the measurement height of most buildings exceeded 10 cm/s2 (gal), with the maximum response reaching 20 gal. Two frequently used methods, i.e., the stochastic subspace identification (SSI) and random decrement technique (RDT) methods are utilized to compare and analyze the amplitude-dependent characteristics of target modal parameters. It is found that with the increase of wind-induced structural vibration amplitude, the fundamental natural frequency generally first decreased and then leveled off, while the damping ratio for the first-order mode of the buildings except the one equipped with a tuned mass damper (TMD) system first increased while then tended to decrease. More interestingly, the critical normalized structural vibration amplitude associated with the maximum damping ratio is found to be in the range of 10−4∼10−5, which agrees well with the theory of “critical tip drift ratio”. Potential explanations for the above phenomena are presented. Furthermore, the obtained results are further compared with existing statistical models, and associated discrepancies suggest the complexities of the dynamic features of supertall buildings.

A systematic approach to modeling synchronous generator using Markov parameters and Takagi–Sugeno fuzzy systems

The problem of precise modeling of Synchronous Generator (SG) devices is demanding and crucial for monitoring, stability, and control of electric grids and microgrids. SGs are known to exhibit nonlinear behavior, and because they may work in a wide range of operating points due to different electric network phenomena like load changes, current intermittent renewable energy resources, temperature variations, topological changes, etc., the modeling task of SG can be a challenging problem. This paper proposes a new method to find a global model for a synchronous generator from the input and output measurement data using state-of-the-art methods in artificial intelligence (AI) like fuzzy clustering, subspace identification, and Takagi–Sugeno (T–S) fuzzy modeling. The fuzzy C-means method is utilized to cluster the measurement data, and then using a subspace identification method based on Markov parameters concepts, the dynamic model of SG for each cluster is obtained in the form of a state space model. A Takagi–Sugeno fuzzy model is applied to determine the corresponding outputs based on the measured inputs and the available state space models. The effectiveness of the proposed approach is illustrated by applying it to the data obtained from simulations on a known fourth-order SG nonlinear model and the data obtained from real-world experimental tests.

A New Paradigm for Structural Characterization, including Rotational Measurements at a Single Site

ABSTRACT In this article, we demonstrate that a single station can be used to measure the dynamic properties of a structure. The station includes a collocated accelerometer and rotational sensor, hence, can record both three-component translation and three-component rotation and is referred to as the 6C-station within this study. The key advantage of this approach is to provide a fast and simple path to a comprehensive structural health monitoring characterization that is comparable to the use of a traditional approach using a horizontal array of three-component accelerometers. The deployment of newly developed high-quality rotational sensors allows the direct measurement of structural rotations, facilitating the extraction of structural mode shapes. In this work, we show how an established system identification tool, stochastic subspace identification, can be applied to the 6C-station data and characterize modal properties and structural response. Our results are verified and contrasted against standard horizontal and vertical array configurations. The Prime Tower, a high-rise structure in Zürich, serves as a case study. A structural characterization of this building is presented for the first time. We show that a 6C-station is capable of defining the frequencies of this stiff high-rise building with a fidelity that is on par with a five-sensor horizontal array. The mode shapes of the roof can be precisely determined with a confidence margin that is comparable to conventional sensing array solutions. However, the effectiveness of using only a 6C-station is determined by the noise level of the sensors—in particular, the rotational seismometer needs to be of high quality. The results indicate that, owing to the collocation measurement of translation and rotation, a 6C-station can deliver a comprehensive structural monitoring solution with minimum time, effort, and footprint.

Distributed Data-Driven Model Predictive Control for Heterogeneous Vehicular Platoon With Uncertain Dynamics

To alleviate the adverse effects of heterogeneous vehicular platoon (HVP) with uncertain dynamics, a distributed data-driven model predictive control (DDMPC) strategy is proposed in this paper. A data-driven model is established with subspace identification using the input-output (I/O) vehicle trajectory. We integrate the data-driven model with the distributed model predictive control (MPC) algorithm to optimize the HVP control. Then, a DDMPC optimal scheme is designed with a target equilibrium and a pair of initial/terminal constraints. Its recursive feasibility and exponential stability are guaranteed by an I/O-to-state stability (IOSS) Lyapunov function and an optimal sum cost function. The string stability analysis of HVP also is provided. Finally, several experiments with heterogeneous vehicular platoon demonstrate the effectiveness of the proposed DDMPC strategy.

Investigating the operational modal response and updating the finite element model of a prototype stone structure

In this work, the analysis of the dynamic behavior of a prototype stone structure has been presented in two ways: (1) the first way is to instrument the structure with two three-component velocity sensors to measure the structure's response to ambient solicitations. An acquisition and processing chain has been developed in our laboratory to record the acquired vibratory signals. The data processing is obtained using different methods of operational modal analysis (OMA) such as Frequency Domain Decomposition (FDD), Random Decrement Technique (RDT), and Stochastic Subspace Identification (SSI). The results obtained by these methods allowed us to extract the modal parameters (damping and natural frequency) of the structure. (2) The second way consists of characterizing the structure's dynamic behavior in a numerical way using Finite Element Modeling (FEM). However, it has often been noted that the experimental dynamic characteristics obtained do not agree with those of the numerical model. The present study aims to extract the dynamic parameters experimentally and numerically and to update the finite element model for stone construction. A good agreement was found between the two approaches.

Stability by assigning structures by applying the multivariable subspace identification algorithm for a wind system with a DFIG

In this paper, a controller for a doubly fed induction generator (DFIG) connected to a wind system is proposed. This control assigning its own structures as an optimal control method, the electric model in the DFIG state space is also shown, for which it is expected to estimate a linear model through the subspace technique and thus to design the controller. It will be possible to show that a structure assignment controller is undoubtedly a good option for the control of multivariable systems. The results of the output signals will be analyzed when applying the controller, assigning their own structures, which will allow us to observe that the response and disturbance times are below two tenths of a second.

A Hybrid Hubspace-RNN based approach for Modelling of Non-Linear Batch Processes

The manuscript addresses the problem of developing a modelling strategy that can accurately capture the dynamics of a non-linear batch process, demonstrated on a uni-axial rotational molding process. To this end, this work presents a strategy that utilizes the nonlinear modeling capability of a recurrent neural network (RNN) model, while leveraging the rigor of subspace-based approaches. The proposed modeling strategy is as follows: a subspace identification algorithm is first utilized on all the training batches to obtain the state sequence for these batches. Then the state sequences from all the training batches and the corresponding input sequences are given as the output and the input to a neural network, respectively. This step essentially builds a non-linear state space model, albeit using the state trajectory identified by the subspace model. The output equation obtained from the above-mentioned subspace identification step along with the newly obtained non-linear state equation is now ready to be used for predicting the output trajectory of the system. The results from the experiments illustrate the improved prediction performance of a model obtained by the proposed hybrid Subspace-RNN approach in comparison to both a subspace-based approach and an RNN-based approach.

Dynamic Parameters Updating of Earth-rock Dams Based on Modal Parameter Identification

The reasonable selection of dynamic parameters of earth-rock dams is very important for the seismic safety assessment of dams. Because of the size effects, the parameters acquired from the indoor test may additionally no longer exactly reflect the real dynamic characteristics of the dam. Therefore, it is essential to correct and update the dynamic parameters in accordance to the actual seismic dynamic characteristics of the dam. In this paper, by combining the Covariance-driven stochastic subspace identification (SSI-COV) method and the multiple population genetic algorithm (MPGA), an optimization and updating method for the dynamic parameters of earth-rock dams based on modal parameter identification is presented. The collected weak earthquake records of the dam allowed the modal parameters (the natural frequencies and mode shapes) identification based on SSI-COV method. The optimization updated is performed using the MPGA, which can obtain the optimal values of dynamic parameters of the dam and has good robustness within the optimization range of the numerical model. A typical numerical example is given to exhibit the feasibility and effectiveness of the presented method. Then the dynamic parameters of Liyutan Dam are updated by the proposed method according to the weak earthquake records, and the accuracy and applicability of the updated parameters were further verified by the strong earthquake records. The results show that the method proposed in this paper can provide a good idea for the calibration of dynamic parameters of earth-rock dams and has well practical engineering value.

Subspace-based modal identification and uncertainty quantification from video image flows

Vibration measurements for structural health monitoring (SHM) by operational modal analysis (OMA) are classically obtained from sensors that are embedded in or physically attached to the monitored structure, like accelerometers or strain gauges. However, the setup time of these sensors and their restricted number and space coverage limit their monitoring capabilities. Video image-based sensing methods can overcome these shortcomings. With adequate image processing methods, motion signals are extracted from video image flows, which are then processed by system identification methods to estimate modal parameters. In this way, the pixels in selected regions of interest within the images act as a dense network of contactless sensors distributed over the whole structure. In this paper, the efficiency of this video-based approach is demonstrated with laboratory experiments on a cantilever beam, in particular, by evaluating its capability for detecting weak damages mimicked by slight mass modifications. To this end, the steerable filter-based method (ST), that recovers displacements from local phase, is first extended to overcome its motion limitation of one pixel size. Then, the performance of the improved motion extraction method is compared with two other well-established methods in the context of OMA, where natural frequencies, damping ratios and mode shapes with high spatial resolution are estimated together with their uncertainty bounds using covariance-driven subspace identification. The compared methods are evaluated with the help of reference laser displacement measurements as well as a finite element model of the beam, revealing differences in the accuracy of the estimated mode shapes depending on the chosen method for motion extraction. Finally, aiming to investigate early structural damage detection, experiments are carried out under small structural changes and the results are compared to a reference state with the help of estimated uncertainties. Small but statistically significant changes in the modal parameters are detected, showing the potential of the vision based framework for SHM.

Streaming Algorithms for Subspace Analysis: Comparative Review and Implementation on IoT Devices

Subspace analysis is a widely used technique for coping with high-dimensional data and is becoming a fundamental step in the early treatment of many signal processing tasks. However, traditional subspace analysis often requires a large amount of memory and computational resources, as it is equivalent to eigenspace determination. To address this issue, specialized streaming algorithms have been developed, allowing subspace analysis to be run on low-power devices such as sensors or edge devices. Here, we present a classification and a comparison of these methods by providing a consistent description and highlighting their features and similarities. We also evaluate their performance in the task of subspace identification with a focus on computational complexity and memory footprint for different signal dimensions. Additionally, we test the implementation of these algorithms on common hardware platforms typically employed for sensors and edge devices.

Indirect measurement of propeller fluctuating forces using an inverse analysis: Numerical and experimental studies

The propeller fluctuating force is being recognized as the dominant source of underwater radiated noise, its accurate acquisition is thus necessitated for a reliable acoustic-structure analysis and optimization of marine ships. However, such dynamic operational forces are frequently impossible or expensive to directly measure due to various practical challenges. To alleviate this limitation, this paper presents an inverse method for the indirect estimation of propeller forces using measured shafting vibration responses. The force reconstruction procedure is constructed based on the state-space model of the propeller–shafting system, which can be derived by a data-driven subspace identification algorithm in conjunction with either the numerical or experimental models of the system. To ensure the robustness of the inverse analysis in the presence of inevitable measurement noise, a modified regularization strategy based on homotopy continuation is introduced. The effectiveness of the proposed algorithm is demonstrated through numerical simulations and experimental investigations. The obtained results demonstrate the potential feasibility of indirect measurement for accurately identifying propeller fluctuating forces in the time domain.

Modal analysis of an operational offshore wind turbine using enhanced Kalman filter‐based subspace identification

AbstractOperational modal analysis (OMA) is an essential tool for understanding the structural dynamics of offshore wind turbines (OWTs). However, the classical OMA algorithms require the excitation of the structure to be stationary white noise, which is often not the case for operational OWTs due to the presence of periodic excitation caused by rotor rotation. To address this issue, several solutions have been proposed in the literature, including the Kalman filter‐based stochastic subspace identification (KF‐SSI) method which eliminates harmonics through estimation and orthogonal projection. In this paper, an enhanced version of the KF‐SSI method is presented that involves a concatenation step, allowing multiple datasets with similar environmental conditions to be used in the identification process, resulting in higher precision. This enhanced framework is applied to an operational OWT and compared to other OMA methods, such as the modified least‐squares complex exponential and PolyMAX. Using field data from a multi‐megawatt operational OWT, it is shown that the enhanced framework is able to accurately distinguish the first three bending modes with more stable estimates and lower variance compared to the original KF‐SSI algorithm and follows a similar trend compared to other approaches.

A Real-Time Monitoring System for Cable Tension with Vibration Signals Based on an Automated Algorithm to Sieve Out Reliable Modal Frequencies

Cables or suspenders are the critical force-transmitting components of cable-supported bridges, and their timely tension monitoring is consequently the most important issue in the corresponding structural health monitoring. However, very few works regarding the full automation of vibration-based tension estimation have been reported in the literature. To develop a monitoring system of cable tension based on real-time vibration signals, this research first employs an efficient stochastic subspace identification (SSI) method with tailored parameter selection to continuously identify the three frequencies of adjacent modes for the cables of Mao-Luo-Hsi Bridge. More importantly, an automated sieving algorithm is delicately established to obtain the stable modal frequencies by making the best of the specific modal frequency distribution for cables. The ratios between the frequency values identified from SSI analysis are exhaustively checked to systematically extract the qualified cable frequencies and decide their corresponding mode orders. The tension is finally computed with one available cable frequency according to the priority order predetermined by the statistics of identification rate. Demonstrated by analyzing the vibration signals measured from the stay cable of Mao-Luo-Hsi Bridge in real time for two full years, the effectiveness and robustness of this real-time monitoring system have been extensively testified. The long-term success rates for the immediate determination of dependable tension are found to be perfect for 15 of the 18 investigated cables. As for the other three cables, their corresponding success rates are still higher than 99.99% with very few cases of absent or false tension values.

Removal of AM-FM harmonics using VMD technology for operational modal analysis of milling robot

The dynamics of a milling robot have a significant impact on machining efficiency and quality. Traditional experimental modal analysis (EMA) is used to study the dynamics of milling robots in the static state. However, the dynamic properties of milling robots change when they are in the operational state. To investigate the dynamics of milling robots during cutting, operational modal analysis (OMA) is used. During normal cutting, milling robots are primarily excited by cutting forces that are dominated by amplitude and frequency-modulated (AM-FM) harmonic components that are caused by the fluctuation of cutting loads and spindle speeds. Such cutting forces make the dynamic parameters identified by OMA inaccurate. To address this issue, the variational mode decomposition-OMA (VMD-OMA) method is proposed herein, which involves removing AM-FM harmonic components from the response signal using the VMD technology and subsequently using the stochastic subspace identification (SSI) algorithm to identify dynamic parameters. To verify the effectiveness of this method, simulations and experimental research have been conducted. The simulation results demonstrate that the dynamic parameters identified by VMD-OMA are generally closer to the theoretical values. Experimental research conducted on a milling robot named TriMule shows that VMD-OMA can effectively eliminate AM-FM harmonics in response signals and identify the dynamic parameters of TriMule during cutting.

Full-parameter constrained parsimonious subspace identification with steady-state information for DC–DC converters

Full-parameter constrained parsimonious subspace identification with steady-state information for DC–DC converters

A Comparative Study of Dynamic Responses of Coastal Long-Span Bridge Under Typhoon with Different Crossing Paths

Coastal long-span bridges are intensively constructed along the western Pacific coast. While the coast is frequently disturbed by typhoons. Given that a coastal long-span bridge will experience a number of typhoons during its service life, it is important to have an understanding of the wind fields formed by typhoons with different crossing paths and corresponding structural dynamic responses. Wind and acceleration data of the Xihoumen Bridge under the influence of onshore, offshore, and landfalling typhoons were acquired by the structural health monitoring system (SHMS). Wind field features of typhoons with three types of paths were compared. The landfalling Typhoon In-fa was used to investigate the differences of wind-induced structural dynamic responses under the influence of each typhoon structural region. The covariance-driven stochastic subspace identification (SSI-COV) was used to identify the modal parameters of the bridge. The results revealed that wind field features at bridge site varied with typhoon crossing paths. The SSI-COV accurately identified the structural frequencies of first 15 vertical modes using the acceleration data under the influence of spiral rainband. The first eyewall has the most detrimental wind conditions to the bridge because the stiffening girder vibrated violently in this region.

Koopman Operator Based Predictive Control With a Data Archive of Observables

Abstract The control of complex systems is often challenging due to high-dimensional nonlinear models, unmodeled phenomena, and parameter uncertainty. The increasing ubiquity of sensors measuring such systems and increased computational resources has led to an interest in purely data-driven control methods, particularly using the Koopman operator. In this paper, we elucidate the construction of a linear predictor based on a sequence of time realizations of observables drawn from a data archive of different trajectories combined with subspace identification methods for linear systems. This approach is free of any predefined set of basis functions but instead depends on the time realization of these basis functions. The prediction and control are demonstrated with examples. The basis functions can be constructed using time-delayed coordinates of the outputs, enabling the application to purely data-driven systems. The paper thus shows the link between Koopman operator-based control methods and classical subspace identification methods. The approach in this paper can be extended to adaptive online learning and control.