Subspace Identification Method Research Articles

Finite element model updating and response prediction of a frame structure based on optimal sensor placement

This paper proposes an approach for finite element (FE) model updating and response prediction of frame structures based on optimal sensor placement (OSP), which integrates sensor placement optimization, mode expansion, and model updating techniques. Firstly, sensor optimization layout and modal testing analysis are conducted on a bolted laboratory frame structure. The covariance-driven stochastic subspace identification (SSI-COV) method identifies the real-world structure’s natural frequencies, modal damping, and mode shapes. Secondly, the complete mode shapes are expanded using the measured incomplete modal data from the limited number of sensors. Thirdly, a multi-objective function based on frequency and mode shapes is established to adjust the parameters of the FE model. This ensures that the updated model accurately represents the dynamic properties of the actual structure within a specific frequency range. Finally, the Rayleigh damping of the frame structure is estimated, and the damping matrix is assembled to enhance the accuracy of dynamic response prediction in the updated model. By comparing the response prediction results of the updated FE model with and without considering the updated damping effects to the measurement data of the real-world structure, it is demonstrated that the proposed method considering updated damping effects can more effectively predict the structural response.

Data-driven replay attack detection for unknown cyber-physical systems

This paper considers a data-driven method to detect stealthy replay attacks on cyber-physical systems (CPSs) whose models are unknown. Most existing attack detection methods assume the system dynamic is known. However, due to the large scale and complexity of the system, it is difficult to get an accurate model of a CPS. This paper uses a moving window subspace identification method to construct a linear discrete time-varying model of CPS. The controllability and observability of the obtained model are proved. On this basis, the replay attack is transformed into a detectable additive attack using the output coding strategy. Then, considering modeling errors, a time-varying H∞ filter is designed, and a detection function based on the output residual is constructed. When the system works without any attacks, the detection function approaches a limited threshold. On the contrary, that function will increase extremely larger than the threshold when the replay attack occurs. The detectability of our scheme for attacks is also mathematically proven. Finally, to verify the effectiveness of the proposed scheme, we provide simulation results on a linear motor system and a nonlinear robotic system.

Mode Shape-Based Damage Detection of Twin Skewed Bridges Based on OMA and FE Model Updating

A comparative study of the dynamic behavior of twin single-span bridges was carried out based on operational modal analysis and a linear finite element model updating with the aim of finding a potential damage indicator. The bridges are skewed, 30 m long and with prestressed concrete girders as the main support structure, but one of them were collided and suffered damage in two of its I-shape girders. Ambient vibration tests were conducted by deploying 14 uniaxial accelerometers along the sidewalks, experimental modal parameters were identified using the COVariance-driven Stochastic Subspace Identification method (SSI-COV). Six vertical modes were clearly identified for each structure. Additionally, some extra modes with non-proportional damping were identified. It was found that the modal frequencies are sensitive to the support conditions and the overall stiffness of the bridge but not to the localized girder damage, which, on the contrary, is reflected in the discrepancy in the fundamental bending mode shape amplitude between the lateral sides of the bridge, and a so-called Continuous Symmetry Measure adopted as a symmetry index seems to be a good damage indicator for this type of straight-alignment simply supported bridges, given the symmetric nature of the bending mode shapes and the asymmetric nature of the damage.

FE Model Updating of Continuous Beam Bridge Based on Response Surface Method

In this paper, A high-order response surface method is proposed for finite element model updating of continuous beam bridges. Firstly, based on visual inspection and environmental vibration testing, the peak picking (PP) method and random subspace identification (SSI) method are used to identify the dynamic characteristic parameters of the structure. Then, the finite element model of the continuous beam bridge is updated based on the third-order response surface method. It can be concluded that the results of the updated finite element model are in good agreement with the test results, and the maximum error between the calculated and measured frequency is less than 3%, with MAC values greater than 85%. Moreover, the updated finite element model can reflect the current situation of real bridges and serve as the basis for bridge health monitoring, damage detection, and safety assessment.

Subspace Identification of Bridge Frequencies Based on the Dimensionless Response of a Two-Axle Vehicle.

As an essential reference to bridge dynamic characteristics, the identification of bridge frequencies has far-reaching consequences for the health monitoring and damage evaluation of bridges. This study proposes a uniform scheme to identify bridge frequencies with two different subspace-based methodologies, i.e., an improved Short-Time Stochastic Subspace Identification (ST-SSI) method and an improved Multivariable Output Error State Space (MOESP) method, by simply adjusting the signal inputs. One of the key features of the proposed scheme is the dimensionless description of the vehicle-bridge interaction system and the employment of the dimensionless response of a two-axle vehicle as the state input, which enhances the robustness of the vehicle properties and speed. Additionally, it establishes the equation of the vehicle biaxial response difference considering the time shift between the front and the rear wheels, theoretically eliminating the road roughness information in the state equation and output signal effectively. The numerical examples discuss the effects of vehicle speeds, road roughness conditions, and ongoing traffic on the bridge identification. According to the dimensionless speed parameter Sv1 of the vehicle, the ST-SSI (Sv1 < 0.1) or MOESP (Sv1 ≥ 0.1) algorithm is applied to extract the frequencies of a simply supported bridge from the dimensionless response of a two-axle vehicle on a single passage. In addition, the proposed methodology is applied to two types of long-span complex bridges. The results show that the proposed approaches exhibit good performance in identifying multi-order frequencies of the bridges, even considering high vehicle speeds, high levels of road surface roughness, and random traffic flows.

An Improved On-Line Recursive Subspace Identification Method Based on Principal Component Analysis and Sliding Window for Polymerization

Polymerization products are indispensable for our daily life, and the relevant modeling process plays a vital role in improving product quality. However, the model identification of the related process is a difficult point in industry due multivariate, nonlinear and time-varying characteristics. As for the conventional offline subspace identification methods, the identification accuracy may be not satisfying. To handle such a problem, an enhanced on-line recursive subspace identification method is presented on the basis of principal component analysis and sliding window (RSIMPCA-SW) in this paper to obtain the state space model for polymerization. In the proposed on-line subspace identification approach, the initial L-factor is acquired by the LQ decomposition of the sampled historical data, firstly, and then it is updated recursively through the bona fide method after the new data have been handled by the sliding window rule. Subsequently, principal component analysis (PCA) is introduced to calculate the extended observation matrix, and finally the on-line model parameters are extracted. Compared with the traditional subspace schemes, smaller computation complexity and higher identification precision are anticipated in the proposed method. A case study on the modeling of the ethylene polymerization verifies the effectiveness of the developed approach, in which the related statistical indexes of the obtained identification model are better.

A novel time-domain approach for identifying nonlinear structural dynamical system with explicit model based on observer/Kalman filter identification method

In this paper, a novel time-domain method for identifying nonlinear structural dynamical system with explicit model is proposed. By exploiting the observer/Kalman filter identification (OKID) and nonlinear feedback interpretation, the nonlinear parameters of the system are estimated accurately. The effectiveness of the proposed nonlinear OKID (NOKID) method is demonstrated through three numerical examples, namely a five degree-of-freedom system with one nonlinear spring, a three degree-of-freedom system with three nonlinear springs and a nonlinear rectangular membrane structure with all edges clamped. Comparing with the time-domain nonlinear subspace identification (TNSI) method, the proposed NOKID method can identify the nonlinear parameters without system order determination, and the identification results obtained by the proposed method are real numbers and have no dependency on frequency.

Evaluation of vibration properties of an 18-story mass timber–concrete hybrid building by on-site vibration tests

Timber–concrete hybrid structural systems are a practical option to provide tall mass timber buildings with a lateral load-resisting system. This paper discusses the dynamic behavior of an 18-story timber–concrete hybrid building based on the vibration properties evaluated by on-site vibration tests. First, microtremor measurements and human-powered excitation tests were carried out and the obtained vibration data were analyzed using a stochastic subspace identification method to derive natural frequencies, damping ratios, and mode shapes. Then, a finite-element (FE) model was developed based on detailed structural design information, and its eigenvalues and eigenvectors were compared with the test results. The vibration test results showed various mode shapes, including in-plane deformation of the floor diaphragm composed of cross-laminated timber (CLT) panels. The damping ratios in all the modes were scattered between 1 and 3%, and no frequency dependency was observed. The modal properties of the FE model agreed well with the test results by considering the additional stiffness of non-structural components. In order to simulate the in-plane deformation of the CLT floor diaphragm, detailed modeling of the connection between each CLT floor panel and the connection between CLT floor panels and concrete cores is recommended. The findings provide practitioners with an insight into dynamic properties and FE modeling methods of tall timber–concrete hybrid buildings.

Control of Distributed Converter-Based Resources in a Zero-Inertia Microgrid Using Robust Deep Learning Neural Network

Considering the evolution of future microgrids (MGs) towards zero-inertia level due to the penetrations of distributed converter-based resources (DCRs), a large number of data produced by these generations will lead the control decisions to be more complicated than conventional power systems. This paper presents a control strategy for a zero-inertia MG with DCRs using a robust deep learning neural network (RDeNN). In a training phase, a sub-space state-based identification method is employed to monitor and analyze the data regarding stability indices, i.e., damping and frequency of dominant modes, and robustness against uncertainties. In addition, a mixed H2/H∞ control strategy is applied to enhance the training efficacy in the frequency and voltage control loops of DCRs. The trained RDeNN is activated to make quick and effective control decisions by using only measured signals from the MG. Simulation results are verified in the zero-inertia MG (or the grid with 100% DCRs) and compared with several existing control techniques. The study results demonstrate the advantages of the proposed RDeNN in many aspects such as low computational time, require-less physical controller models, fast and flexible stabilizing responses, and high robustness against various time delays, data quality issues, and MG uncertainties.

Adaptive Constraint Penalty-Based Multiobjective Operation Optimization of an Industrial Dynamic System With Complex Multiconstraint.

Aiming at the operation optimization of the wastewater treatment process (WWTP) with nonstationary time-varying dynamics and complex multiconstraint, this article proposes a novel adaptive constraint penalty decomposed multiobjective evolutionary algorithm with synthetical distance (SD)-based cross-generation crossover. First, the concept of spatial SD is presented to comprehensively evaluate the similarity of individual solutions from two aspects of distance and angle, and the individual information between two adjacent generations is used to enhance the diversity of individuals and accelerate the convergence of the algorithm. Second, aiming at the complex multiconstraint during the operation optimization of WWTP, an adaptive penalty algorithm is further adopted to punish the individual solutions that violate the constraints, so as to improve the handling efficiency and success rate of constraints. Furthermore, in view of the time-varying dynamics of actual WWTP, a recursive bilinear subspace identification method based on sliding window is adopted to establish the optimization models as well as the constraint models with self-learning parameter, which provides accurate model guarantee for high-performance multiobjective operation optimization. Finally, the effectiveness, superiority, and practicability of the proposed method are verified through test function experiments as well as operation optimization control experiments of WWTP.

Recursive Delta-Operator-Based Subspace Identification with Fixed Data Size

This paper proposes a recursive delta-operator-based subspace identification method with fixed data size. The majority of existing subspace identification methods are constrained to discrete-time systems because of the disparity in Hankel matrices. Additionally, due to the storage cost, LQ-factorization and singular value decomposition in identification methods are best suited for batch processing rather than online identification. The continuous-time systems are transformed into state space models based on the delta-operator to address these issues. These models approach the original systems when the sampling interval approaches zero. The size of the data matrices is fixed to reduce the computing load. By fading the impact of past data on future data, the amount of data storage can be decreased. The effectiveness of the proposed method is illustrated by the continuous stirred tank reactor system.

The added mass of a biaxial tensioned membrane in still air

It is well known that added mass significantly impacts the vibration of membrane structures in still air. Numerous theoretical, numerical, and experimental studies have been conducted on the added mass of axial tensioned membranes. However, the added mass of biaxial tensioned membranes subjected to different tensile forces in two directions in still air remains unclear. Therefore, this study focuses on investigating the added mass of biaxial tensioned membranes in still air. Firstly, this paper proposes a simplified theoretical model for the added mass of biaxial tensioned membranes in still air based on the energy conservation law. To validate the accuracy of the proposed model, a modal testing system for a rectangular membrane is designed to identify the frequencies of biaxial tensioned membranes in still air. In the experimental system, the utilization of a laser displacement sensor array is to obtain the time-displacement information of observation points. Then, a combination of Fast Fourier Transform (FFT) and Stochastic Subspace Identification (SSI) methods is employed for modal identification. Comparative analysis between the experimental and theoretical model results demonstrates an excellent agreement in frequencies. Additionally, the proposed added mass model is closer to the experimental added mass than other models, with a maximum deviation of only 4.77 %. This research provides a reference for the study of the impact of air on the ground vibration of membranes.

Closed-Loop Continuous-Time Subspace Identification with Prior Information

This paper presents a closed-loop continuous-time subspace identification method using prior information. Based on a rational inner function, a generalized orthonormal basis can be constructed, and the transformed noises have ergodicity features. The continuous-time stochastic system is converted into a discrete-time stochastic system by using generalized orthogonal basis functions. As is known to all, incorporating prior information into identification strategies can increase the precision of the identified model. To enhance the precision of the identification method, prior information is integrated through the use of constrained least squares, and principal component analysis is adopted to achieve the reliable estimate of the system. Moreover, the identification of open-loop models is the primary intent of the continuous-time system identification approaches. For closed-loop systems, the open-loop subspace identification methods may produce biased results. Principal component analysis, which reliably estimates closed-loop systems, provides a solution to this problem. The restricted least-squares method with an equality constraint is used to incorporate prior information into the impulse response following the principal component analysis. The input–output algebraic equation yielded an optimal multi-step-ahead predictor, and the equality constraints describe the prior information. The effectiveness of the proposed method is provided by numerical simulations.

Comparison of Subspace Identification Methods for Modal Estimation of Bladed Disks

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

Numerical and experimental study on the dynamic equivalent methodology of a membrane antenna structure and a grid membrane structure

The dynamic equivalent methodology utilizing a grid membrane substitute for a planar membrane for vibration test verification on the ground has been demonstrated in small sizes with simple constraints. The method lacks accuracy and validity for a real complex membrane antenna. This paper thus focuses on the applicability of the equivalence approach to a membrane antenna and the factors affecting its dynamic equivalence to verify whether the grid membrane structure can replace the membrane antenna structure for modal identification on the ground. To this end, an experimental system is developed to conduct vibration tests on the grid membrane structure in air, using the grid membrane model with unidirectional tension as a substitute for the membrane array. The connecting strips attach the grid membrane to thin-walled lenticular booms (TWLBs) to allow for unidirectional tension. A laser displacement sensor array is employed to obtain the vibration data. A combination of the Fast Fourier Transfer (FFT) and Stochastic Subspace Identification (SSI) methods is applied to identify the structural frequencies and mode shapes. Vibration tests on the grid membranes with different added masses and tensile forces are conducted. Meanwhile, the numerical results for the rectangular membrane are chosen as a reference for comparison with the experimental results for the grid membrane. In conclusion, the numerical results for the membrane antenna structure and the experimental results for the grid membrane structure show good agreement in terms of frequency and mode shape. Additionally, both the added masses in the intersection areas of the grid membrane and the tensile force have a significant effect on the dynamic equivalence.

Correlation Analysis of Large-Span Cable-Stayed Bridge Structural Frequencies with Environmental Factors Based on Support Vector Regression

The dynamic characteristics of bridge structures are influenced by various environmental factors, and exploring the impact of environmental temperature and humidity on structural modal parameters is of great significance for structural health assessment. This paper utilized the Covariance-Driven Stochastic Subspace Identification method (SSI-COV) and clustering algorithms to identify modal frequencies from four months of acceleration data collected from the health monitoring system of the Jintang Hantan Twin-Island Bridge. Furthermore, a correlation analysis is conducted to examine the relationship between higher-order frequency and environmental factors, including temperature and humidity. Subsequently, a Support Vector Machine Regression (SVR) model is employed to analyze the effects of environmental temperature on structural modal frequencies. This study has obtained the following conclusions: 1. Correlation analysis revealed that temperature is the primary influencing factor in frequency variations. Frequency exhibited a strong linear correlation with temperature and little correlation with humidity. 2. SVR regression analysis was performed on frequency and temperature, and an evaluation of the fitting residuals was conducted. The model effectively fit the sample data and provided reliable predictive results. 3. The original structural frequencies underwent smoothing, eliminating the influence of temperature-induced frequency data generated by the SVR model. After eliminating the temperature effects, the fluctuations in frequency within a 24 h period significantly decreased. The data presented in this paper can serve as a reference for further health assessments of similar bridge structures.

Continuous-Time Subspace Identification with Prior Information Using Generalized Orthonormal Basis Functions

This paper presents a continuous-time subspace identification method utilizing prior information and generalized orthonormal basis functions. A generalized orthonormal basis is constructed by a rational inner function, and the transformed noises have ergodic properties. The lifting approach and the Hambo system transform are used to establish the equivalent nature of continuous and transformed discrete-time stochastic systems. The constrained least squares method is adopted to investigate the incorporation of prior knowledge in order to further increase the subspace identification algorithm’s accuracy. The input–output algebraic equation derives an optimal multistep forward predictor, and prior knowledge is expressed as equality constraints. In order to solve an optimization problem with equality constraints characterizing the prior knowledge, the proposed method reduces the computational burden. The effectiveness of the proposed method is provided by numerical simulations.

A multivariate nonlinear dynamic programming of female figures in Qing dynasty literature

Abstract To improve the recognition of female images in Qing Dynasty literature, this paper designs a multivariate nonlinear-based image dynamic programming model. Data-driven typical correlation analysis is used to extract the key controllable variables with the strongest correlation with female image features and use them as input variables for modeling so as to make the maximum correlation between different image features and improve the modeling efficiency. The nonlinear spatial state model is established by using the subspace identification method, and the female image planning model is substituted into the multivariate nonlinear analysis, and the parameters of the nonlinear fitting function about the image planning can be obtained. The simulation analysis of the image dynamic planning model based on multivariate nonlinearity is carried out, and the results show that the average annual failure time of the model designed in this paper is 12.6 hours, and the classification accuracy in female image classification is 96.3%, and the classification time is stable at 1.162 s. The results show that the multivariate nonlinear features of the model can carry out dynamic planning of female images in Qing dynasty literature and improve the classification of image feature recognition.

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 timedelayed 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.

Enhanced semi-automated Bayesian modal identification approach for Ultra-high voltage transmission towers

The accuracy and efficiency of the modal identification for Ultra-high voltage (UHV) transmission towers under harsh operational environments is seriously affected by environmental noises. In general, the initial natural frequency drowned in the noises is evaluated by the experience of engineers before performing a Bayesian modal identification approach. It will lead to potential errors and limitations to the application of the Bayesian modal identification approach. In this study, a coherent clustering enhanced semi-automated Bayesian modal identification method is proposed and then implemented in the operational modal analysis of an instrumented UHV transmission tower under ambient excitation. The coherent clustering is adopted to obtain the quantitative value of the initial natural frequency, in place of the empirical evaluation. Then, the Fast Bayesian Fast Fourier Transform (FBFFT) method could accurately identify the most probable values (MPV) and the corresponding posterior uncertainty of modal parameters. Moreover, the first ten modes of the UHV transmission tower are identified, and the results of modal parameters are compared to the stochastic subspace identification (SSI) method. The results show that the coherent clustering enhanced semi-automated Bayesian method could accurately identify modal parameters with posterior uncertainty, even for modes weakly excited. The proposed method could provide a reliable basis for the modal updating, damage detection, and dynamic reliability assessment of UHV transmission towers.