Subspace Identification Algorithm Research Articles

Enhanced predictive PDF control of stochastic distribution systems with neural network compensation and its application

Compared to the conventional control algorithms that use mean and variance as indicators, predictive probability density function (PDF) control can effectively handle the output PDF control problem of non-Gaussian stochastic distribution systems. However, the existing predictive PDF control method does not consider the construction error between output PDF and weight, thus the control performance is still unsatisfactory. Therefore, this paper proposes a new Enhanced Predictive PDF control method (En-PDF) to improve the output PDF control performance of stochastic distribution systems. The proposed method mainly consists of two parts: the predictive PDF control part and the neural network compensation control part aiming to reduce the bias of output PDF. First, the Radical Basis Functions (RBFs) are used to approximate the PDF of the stochastic systems output, and then a prediction model representing the relationship between input and weight is established using the subspace identification algorithm to design the predictive PDF control for the stochastic systems. Next, the Kullback-Leibler (KL) divergence is used to measure the similarity between the output PDF and the set PDF, combined with the weight error and compensation to design a new performance index. Based on this, the parameters of the neural network are adjusted using the gradient descent algorithm to obtain the optimal compensation, and the stability and tracking performance of the proposed algorithm are analyzed using inductive reasoning method. Finally, the predictive PDF control input with the compensation work together on the controlled plant to achieve high-performance control of the output PDF of non-Gaussian stochastic distribution systems. Both simulation experiments and physical control experiments validate the effectiveness and superiority of the proposed method.

Study of Experimental and Assembly Uncertainties on Modal Parameter Estimates of Axial Piston Pumps

Finite Element Model Updating (FEMU) plays a pivotal role in enhancing the accuracy and reliability of structural dynamics models. Nonetheless, uncertainties related to experimental vibration testing and natural manufacturing variability introduce unavoidable variability in the results of Modal Parameter Extraction (MPE), which is the basis for updating. In this regard, this study delves into the inherent variability of estimates from MPE following from experimental vibration testing Axial Piston Pumps (APPs). Accordingly, we investigate the effect of material properties, boundary conditions and measurement noise, through several experimental vibration tests involving assembly-disassembly and exchange of components. These variations account for inherent manufacturing variability and tolerances both at the component and material level. The obtained vibration data is processed using non-parametric FRF estimates and the Stochastic Subspace Identification (SSI) algorithm, resulting in a collection of FRFs and modal parameter estimates (natural frequencies, damping ratios and mode shapes). We use multivariate analysis techniques to quantify the uncertainty of these estimates and to assess the individual effect of assembly and population uncertainties. These results serve as a basis for further investigation towards the updating of a FE model of the APP, and the quantification of modal parameter uncertainties within the material and substructure connectivity properties.

Wear parameters identification of hydrodynamic bearing based on operational modal analysis and on-rotor sensing technology

Abrasive wear is a predominant fault in hydrodynamic bearings that can deteriorate bearing performance and damage the rotating machine eventually. The present work proposes a novel wear parameters identification method for hydrodynamic bearings based on operational modal analysis (OMA) and on-rotor sensing (ORS) technology. With this framework, the objective function is defined as the sum of squared errors between the theoretical modal frequencies and the identified modal frequencies. For the experiment verification, the ORS technology is used to collect rotor vibration directly. Additionally, the cepstrum editing procedure (CEP) is applied to enhance modal information. The different wear parameters are successfully identified using combined stochastic subspace identification (SSI) and particle swarm optimization (PSO) algorithms in both simulation and experimental signals.

Automated operational modal analysis for supertall buildings based on a three-stage strategy and modified hierarchical clustering

Several automated operational modal analysis (AOMA) methods have been developed to evaluate the dynamic characteristics of large-scale structures in real-time under environmental and operational variations. Typically, these methods need to manually set some thresholds to achieve automatic identification. However, there is a lack of uniform standards for setting these thresholds, which may result in the adoption of inappropriate settings in AOMA, thereby introducing errors in modal identification. To address this issue, this paper proposes a novel AOMA framework to automatically identify modal parameters, which mainly involves three steps. Firstly, the covariance-driven stochastic subspace identification (Cov-SSI) algorithm is employed to perform modal estimation based on measured ambient vibration records. Then, a three-stage strategy, including hard validation criteria, Gaussian mixture model clustering-driven soft validation criteria, and the local outlier factor algorithm, is presented to remove spurious modes and determine real physical modes. Finally, a modified hierarchical clustering based on the k-nearest neighbor information is applied to group the determined physical modes to achieve automatic modal identification. The effectiveness of the proposed AOMA framework in automatically identifying modal parameters is validated through a numerical simulation study for a five-floor frame structure. Furthermore, the proposed framework is applied to evaluate the modal properties of a 600 m high supertall building based on long-term monitoring records. The results show that the AOMA framework can effectively remove spurious modes and group physical modes, thus identifying the modal parameters with high accuracy. In short, the proposed AOMA framework is an effective tool for modal identification applied in field measurements or structural health monitoring.

Multimodal subspace identification for modeling discrete-continuous spiking and field potential population activity

Objective. Learning dynamical latent state models for multimodal spiking and field potential activity can reveal their collective low-dimensional dynamics and enable better decoding of behavior through multimodal fusion. Toward this goal, developing unsupervised learning methods that are computationally efficient is important, especially for real-time learning applications such as brain–machine interfaces (BMIs). However, efficient learning remains elusive for multimodal spike-field data due to their heterogeneous discrete-continuous distributions and different timescales. Approach. Here, we develop a multiscale subspace identification (multiscale SID) algorithm that enables computationally efficient learning for modeling and dimensionality reduction for multimodal discrete-continuous spike-field data. We describe the spike-field activity as combined Poisson and Gaussian observations, for which we derive a new analytical SID method. Importantly, we also introduce a novel constrained optimization approach to learn valid noise statistics, which is critical for multimodal statistical inference of the latent state, neural activity, and behavior. We validate the method using numerical simulations and with spiking and local field potential population activity recorded during a naturalistic reach and grasp behavior. Main results. We find that multiscale SID accurately learned dynamical models of spike-field signals and extracted low-dimensional dynamics from these multimodal signals. Further, it fused multimodal information, thus better identifying the dynamical modes and predicting behavior compared to using a single modality. Finally, compared to existing multiscale expectation-maximization learning for Poisson–Gaussian observations, multiscale SID had a much lower training time while being better in identifying the dynamical modes and having a better or similar accuracy in predicting neural activity and behavior. Significance. Overall, multiscale SID is an accurate learning method that is particularly beneficial when efficient learning is of interest, such as for online adaptive BMIs to track non-stationary dynamics or for reducing offline training time in neuroscience investigations.

Structural flexibility identification from impact test data through a subband estimation method

SummaryFlexibility is an important parameter reflecting bridge load‐carrying capacity. Dynamic testing is a fast and effective method to obtain the structural modal flexibility of small‐ and medium‐span bridges. The Deterministic‐stochastic subspace identification (DSI) algorithm is a well‐established structure identification method in the time domain. However, the estimation of damping, especially the modal scaling factor, is not always reliable due to inevitable measurement noise, which directly affects the identification accuracy of flexibility. This paper proposes a maximum likelihood estimation method in subbands (SMLE), which can be regarded as an add‐on method of the DSI algorithm because the initial parameters are obtained from the DSI algorithm. The processing of frequency band division is implemented first, and the frequency response function curve in each subband of the whole frequency range is fit separately. Then, subband cyclic iteration is proposed to improve the identification accuracy in a closely spaced mode system. The proposed SMLE method maintains the advantages of the DSI algorithm while improving the accuracy of parameter estimation and flexibility identification. Two lumped mass models are used to verify that the proposed method can effectively improve estimates to obtain a precise flexibility matrix and predict the displacement of the structure under static loading. Experimental example of a continuous girder bridge is considered to verify the availability and effectiveness of the proposed method in practice.

A hybrid output-only scheme for precise modal estimation and uncertainty quantification of large-scale structure through vibration-based measurements

In structural health monitoring or operational modal analysis, owing to unknown or unmeasured ambient excitation information, only structural responses are typically available for modal identification. In this context, bias and variance (uncertainty) errors inevitably exist in modal estimates (especially damping estimates), resulting in inaccurate determinations of structural dynamic properties. To this end, a hybrid output-only scheme based on the second-order blind identification, block bootstrap, and enhanced covariance-driven stochastic subspace identification algorithm with first-order perturbation is presented in this paper to perform precise modal estimation and uncertainty quantification. The accuracy and effectiveness of the hybrid scheme in performing modal identification are verified by numerical simulation study of a framework structure. Furthermore, the hybrid method is applied to analyze recorded acceleration responses of a supertall building with 600 m height during Typhoon Kompasu by considering different sensor setups to verify its applicability and robustness in practical applications, and further investigates the dynamic properties of the skyscraper and their variations during the typhoon. The numerical simulation and field measurement studies demonstrate that the hybrid scheme can effectively reduce the bias errors and quantify the variance errors in modal estimates through a single ambient vibration test, thereby improving the confidence and accuracy of modal identification. Notably, the hybrid method is an effective tool to perform high-accuracy modal estimation and uncertainty quantification for large-scale structures under ambient excitations.

Machine-learning-driven automatic application of the stochastic subspace identification method

Vibration-based operational modal analysis (OMA) methods have been proven effective in identifying dynamic properties of existing structures and infrastructures under operational conditions. Nevertheless, the provision and installation of continuous monitoring systems for long-term structural health monitoring (SHM) purposes potentially applicable to the entire infrastructure networks or to the regional scale of existing vulnerable building heritage require significant economic planning efforts. Nowadays research trends are oriented toward developing effective automatic OMA (AOMA) methods for setting up novel and efficient long-term SHM solutions. The current study illustrates a new recent paradigm for the automatic output-only modal identification of linear structures under ambient vibrations called intelligent automatic operational modal analysis (i-AOMA). The proposed approach relies on the covariance-based stochastic subspace identification (SSI-cov) algorithm and effectively integrates a machine learning intelligent core, i.e. a random forest (RF) classifier, in a conceptually two steps procedure, i.e. an explorative phase and an intelligently-driven phase. The i-AOMA procedure provided a new framework that requires a minimum intervention to the user and is potentially able to deliver uncertainty measures of the modal parameters’ estimates based on the explored SSI-cov control parameters. An application on a shear-type RC frame building typical of existing heritage in Italy is herein discussed and reported.

A Weighted Least-Squares Method for Non-Asymptotic Identification of Markov Parameters from Multiple Trajectories

Markov parameters play a key role in system identification. There exists many algorithms where these parameters are estimated using least-squares in a first, pre-processing, step, including subspace identification and multi-step least-squares algorithms, such as Weighted Null-Space Fitting. Recently, there has been an increasing interest in non-asymptotic analysis of estimation algorithms. In this contribution we identify the Markov parameters using weighted least-squares and present non-asymptotic analysis for such estimator. To cover both stable and unstable systems, multiple trajectories are collected. We show that with the optimal weighting matrix, weighted least-squares gives a tighter error bound than ordinary least-squares for the case of non-uniformly distributed measurement errors. Moreover, as the optimal weighting matrix depends on the system’s true parameters, we introduce two methods to consistently estimate the optimal weighting matrix, where the convergence rate of these estimates is also provided. Numerical experiments demonstrate improvements of weighted least-squares over ordinary least-squares in finite sample settings.

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.

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.

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.

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.

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.

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.

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.

Investigation of long-term modal properties of a supertall building under environmental and operational variations

The information on long-term modal properties of civil structures under environmental and operational variations is generally required in structural health monitoring and vibration control. In operational modal analysis (OMA), damping estimates usually present larger fluctuations and uncertainties than natural frequency and mode shape estimates, which affects the precise determination of the long-term damping characteristics of civil structures. To this end, a combined OMA scheme is adopted in this paper based on the variational mode extraction technique and covariance-driven stochastic subspace identification algorithm to reduce errors in modal identification, especially for damping estimates. Through numerical simulation study of a three-story frame structure, the effectiveness and accuracy of the combined scheme for modal estimations are validated. Moreover, the combined approach is further utilized to evaluate the long-term modal properties of a 600 m high skyscraper under environmental and operational variations from the measured response records of 183 days. Based on the reliable modal estimates by the combined method, the effects of environmental factors (air temperature and relative humidity), wind conditions, and building response amplitudes on the long-term modal properties and their statistical characteristics are investigated in detail. This paper aims to provide an effective tool for analyzing the long-term modal properties of civil structures and further reveal the time evolution of the dynamical characteristics of supertall buildings under environmental and operation variations. • Present a combined scheme based on variational mode extraction technique and covariance-driven stochastic subspace identification algorithm to reduce errors in structural modal estimates. • Suggest an empirical formula for determining minimum length of responses required for accurate modal estimates. • Validate effectiveness and accuracy of the combined scheme via numerical simulation study. • Investigate long-term evolution of dynamical characteristics of a 600 m high skyscraper under environmental and operational variations.

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

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

Practical Implementation of Recursive Subspace Identification on Seismically Excited Structures with Fixed Window

As one of the most catastrophic natural disasters worldwide, earthquakes and their effect on structures are very important to structural health monitoring (SHM), particularly for the ones living around the Pacific ring of fire. In this regard, SHM techniques with real-time or online processing can be used to identify states of structures, track modal parameters, provide a warning message about damage, and help post-earthquake reconnaissance and rehabilitation. For instance, a recursive formulation based on subspace identification (SI) has been demonstrated that it is capable to track system changes. In this study, a recursive subspace identification (RSI) algorithm with a fixed window is proposed to investigate the time-varying dynamic characteristics under seismic excitations. Subsequently, some suggestion is described and discussed for practical implementation. For verifying the proposed algorithm, different datasets from full-scale experiments are applied to examine its applicability. In other words, the practicability of implementing RSI in real-time or online has been developed and examined in this paper.