observer/Kalman Filter Identification Research Articles

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.

Interval type-2 evolving fuzzy Kalman filter for processing of unobservable spectral components from uncertain experimental data

In this paper, an interval type-2 evolving fuzzy Kalman filter (IT2EFKF) is designed for processing unobservable spectral components of uncertain experimental data. The primary objective of the methodology proposed in the present research is to provide a novel mathematical tool for interval and spectral processing of uncertain experimental data in order to deal with real-world filtering, tracking, and forecasting problems. The adopted methodology consider the following steps: an initial model of the interval type-2 fuzzy Kalman filter, which is off-line identified from an initial window of the experimental data; the updating of antecedent proposition of interval type-2 fuzzy Kalman filter by using an interval type-2 formulation of evolving Takagi–Sugeno (eTS) clustering algorithm and the updating of consequent proposition by using a type-2 fuzzy formulation of Observer/Kalman Filter Identification (OKID) algorithm, taking into account the multivariable recursive Singular Spectral Analysis of the experimental data. Computational results for tracking the Mackey-Glass chaotic time series demonstrate the effectiveness of the proposed approach when compared to related methodologies from the literature, with superior results for RMSE of 0.0026. Experimental results for tracking a 2DoF helicopter illustrate its applicability, with superior results for RMSE and VAF of 0.00156 and 99.9874% for yaw angle, and of 0.00702 and 99.8863% for pitch angle, respectively.

Type-2 evolving fuzzy Kalman filter design based on unobservable spectral components space for interval tracking of non-stationary experimental data

In this paper, an interval type-2 evolving fuzzy Kalman filter is designed for processing of unobservable spectral components of uncertain experimental data. The adopted methodology consider the following steps: an initial model of the interval type-2 fuzzy Kalman filter, which is off-line identified from an initial window of the experimental data; the updating of antecedent proposition of interval type-2 fuzzy Kalman filter by using an interval type-2 formulation of evolving Takagi-Sugeno (eTS) clustering algorithm and the updating of consequent proposition by using a type-2 fuzzy formulation of Observer/Kalman Filter Identification (OKID) algorithm, taking into account the multivariable recursive Singular Spectral Analysis of the experimental data. The computational results for tracking the Mackey-Glass chaotic time series illustrate the efficiency of proposed methodology as compared to relevant approaches from literature, and the experimental results for tracking a 2DoF helicopter demonstrate its applicability.

Estimation of Dynamical Thermoacoustic Modes Using an Output Only Observer Kalman Filter-Based Identification Algorithm

Abstract Thermoacoustic instabilities have plagued the operation of gas turbine engines for years and significant research is being conducted in detecting and understanding them. In this paper, an output only identification technique is employed for a noise induced dynamical system representing combustion instability behavior. This approach is called the output only observer Kalman filter identification (O3KID) and its first step solves for least squares from a set of algebraic equations constructed from just the measured output. The least squares solution gives the Markov parameters (impulse response) and the output residuals. The subsequent step takes the Markov parameters or the residuals to solve for the system matrices using any deterministic subspace identification method. In using this direct noniterative two-step algorithm, it is possible to estimate the eigenmodes and damping coefficients from output measured data. To validate the algorithm, a system of independent harmonic oscillators, excited by random noise is used to generate surrogate data representing pressure oscillations in a combustor prior to an instability. The error in estimating the eigen frequencies and damping are <1%. This fast direct approach could be used to provide an early warning indicator in industrial gas turbines by tracking the rate of damping of dominant eigenmodes. Additionally, saving the state space parameters periodically can serve as a data-lean option to track changes of the dynamics and across a gas turbine fleet.

National innovation systems and dynamic impact of institutional structures on national innovation capability: A configurational approach with the OKID method

Understanding the national innovation capability involves the consideration of a variety of evolving institutional structures within the national innovation system (NIS). The variety of and interactions among institutional structures requires a systemic and dynamic approach to the NIS. In this respect, a configurational approach generates specific configurational conditions of the institutional structures, and offers a comprehensive and integrated approach to deal with the inherently complex and evolving nature of the NIS. In this research, using the Global Innovation Index (GII) data, we employ a fuzzy model with the Observer Kalman filter identification (OKID) method to develop configurational combinations. Our analysis provides a characterization of the impact of specific institutional structures on national innovation capability, while accounting for time and the innovation level of the countries. By explaining which specific institutional structures impact national innovation capability, this study contributes to the design of the innovation systems with a systemic approach and our understanding of which institutional structures to support innovation.

Interval type-2 fuzzy computational model for real time Kalman filtering and forecasting of the dynamic spreading behavior of novel Coronavirus 2019

This paper presents a computational model based on interval type-2 fuzzy systems for analysis and forecasting of COVID-19 dynamic spreading behavior. The proposed methodology is related to interval type-2 fuzzy Kalman filters design from experimental data of daily deaths reports. Initially, a recursive spectral decomposition is performed on the experimental dataset to extract relevant unobservable components for parametric estimation of the interval type-2 fuzzy Kalman filter. The antecedent propositions of fuzzy rules are obtained by formulating a type-2 fuzzy clustering algorithm. The state space submodels and the interval Kalman gains in consequent propositions of fuzzy rules are recursively updated by a proposed interval type-2 fuzzy Observer/Kalman Filter Identification (OKID) algorithm, taking into account the unobservable components obtained by recursive spectral decomposition of epidemiological experimental data of COVID-19. For validation purposes, through a comparative analysis with relevant references of literature, the proposed methodology is evaluated from the adaptive tracking and forecasting of COVID-19 dynamic spreading behavior, in Brazil, with the better results for RMSE of 1.24×10−5, MAE of 2.62×10−6, R2 of 0.99976, and MAPE of 6.33×10−6.

Kalman filter identification method for micro-vibration transfer paths of satellites

Micro-vibrations on-board a satellite have degrading effects on the performance of certain payloads like observation cameras. The major sources of vibrations include momentum wheels, solar array drives, other rotary mechanical equipment, etc. These vibrations result in loss of the pointing precision and image quality of the payload through intricate transfer paths. To improve the accuracy of a satellite system with many vibration sources and complex transfer paths, it is necessary to determine the main transfer path of vibration. In this study, a path identification method is proposed and applied to the transfer system from the momentum wheel to the camera mount. First, the observer/Kalman filter identification (OKID) algorithm is used to acquire the state-space equation of each path subsystem. Then, the subsystem order is obtained based on the slope of the singular entropy increment. In the next phase, combined with the measured disturbance force of the momentum wheel, the displacement response of the target point is predicted. Finally, the dominant transfer path of vibration is achieved by calculating the vibration contribution of each path to the response point. The results indicate that the dominant transfer path is the axial path of the horizontal momentum wheel, which contributes to the vibration of the camera mount at most. Effective vibration reduction measures should be taken to this path to suppress the vibration signal. In comparing the identified displacement response with the finite element response of the camera mount under different noise conditions, the correlation coefficients are >0.85, which proves the accuracy and anti-noise capability of the identification method.

A novel interval type-2 fuzzy Kalman filtering and tracking of experimental data.

In this paper, a methodology for design of fuzzy Kalman filter, using interval type-2 fuzzy models, in discrete time domain, via spectral decomposition of experimental data, is proposed. The adopted methodology consists of recursive parametric estimation of local state space linear submodels of interval type-2 fuzzy Kalman filter for tracking and forecasting of the dynamics inherited to experimental data, using an interval type-2 fuzzy version of Observer/Kalman Filter Identification (OKID) algorithm. The partitioning of the experimental data is performed by interval type-2 fuzzy Gustafson–Kessel clustering algorithm. The interval Kalman gains in the consequent proposition of interval type-2 fuzzy Kalman filter are updated according to unobservable components computed by recursive spectral decomposition of experimental data. Computational results illustrate the efficiency of proposed methodology for filtering and tracking the time delayed state variables of Chen’s chaotic attractor in a noisy environment, and experimental results illustrate its applicability for adaptive and real time forecasting the dynamic spread behavior of novel Coronavirus 2019 (COVID-19) outbreak in Brazil.

Synergistic bridge modal analysis using frequency domain decomposition, observer Kalman filter identification, stochastic subspace identification, system realization using information matrix, and autoregressive exogenous model

This paper presents multiple system identification of large-scale bridge structures proposing the combined usage of different modal parameter findings, namely from Frequency Domain Decomposition, Observer Kalman Filter Identification/Eigensystem Realization Algorithm, Combined Deterministic Stochastic Subspace Identification, System Realization Using Information Matrix, and Autoregressive Exogenous Model. A method-centric democratic ranking approach visualizes and quantifies the harmony among different system identification methods in terms of modal parameters, then ranks them based on the correlation among each other, and consequently complies with the highest rank modal parameter outputs. The synergistic scheme is applied on a numerical beam and two bridge structures including one healthy and another subjected to progressive damage. Looking at the top-rank selections, one can see that outlier identification results from a population of modal parameters can intuitively become extinct. The collaboration among methods is dependent on the chosen methods; therefore, method selection relies on care and fair representation of the identification features. Lack of agreement between methods can indicate low confidence in the outranking method and is quantified by median absolute deviation. Nevertheless, the majority of the algorithm population agrees on specific results, which are valuable to produce state knowledge despite low signal to noise ratio, especially without the presence of a reference. Thus, the collaborative usage of multiple methods in a systematic and ranking-based manner reduces significant error and outlier possibilities in modal identification due to algorithm-related issues, which is the novel contribution of this study.

Structural and Crack Parameter Identification on Structures Using Observer Kalman Filter Identification/Eigen System Realization Algorithm

Structural and crack parameters in a continuous mass model are identified using Observer Kalman filter Identification (OKID) and Eigen Realization Algorithm (ERA). Markov parameters are extracted from the input and out responses from which the state space model of the structural system is determined using Hankel matrix and singular value decomposition by Eigen Realization algorithm. The structural parameters are identified from the state space model. This method is applied to a lumped mass system and a cantilever which are excited with a harmonic excitation at its free end and the acceleration responses at all nodes are measured. The stiffness and damping parameters are identified from the extracted matrices using Newton-Raphson method on the structure. Later, cracks are introduced in the cantilever and all structural parameters are assumed as known priori, the unknown crack parameters such as normalized crack depth and its location are identified using OKID/ERA. The parameters extracted by using this algorithm are compared with other structural identification methods available in the literature. The main advantage of this algorithm is good accuracy of identified structural parameters.

Machine Learning Model for Computational Tracking and Forecasting the COVID-19 Dynamic Propagation.

A computational model with intelligent machine learning for analysis of epidemiological data, is proposed. The innovations of adopted methodology consist of an interval type-2 fuzzy clustering algorithm based on adaptive similarity distance mechanism for defining specific operation regions associated to the behavior and uncertainty inherited to epidemiological data, and an interval type-2 fuzzy version of Observer/Kalman Filter Identification (OKID) algorithm for adaptive tracking and real time forecasting according to unobservable components computed by recursive spectral decomposition of experimental epidemiological data. Experimental results and comparative analysis illustrate the efficiency and applicability of proposed methodology for adaptive tracking and real time forecasting the dynamic propagation behavior of novel coronavirus 2019 (COVID-19) outbreak in Brazil.

Computational Approach For Real-Time Interval Type-2 Fuzzy Kalman Filtering and Forecasting via Unobservable Spectral Components of Experimental Data

In this paper, a methodology for design of Kalman filter, using interval type-2 fuzzy systems, in discrete time domain, via spectral decomposition of experimental data, is proposed. The adopted methodology consists of recursive parametric estimation of local state space linear submodels of interval type-2 fuzzy Kalman filter for tracking and forecasting of the dynamics inherited to experimental data, using an interval type-2 fuzzy version of Observer/Kalman Filter Identification (OKID) algorithm. The partitioning of the experimental data is performed by interval type-2 fuzzy Gustafson–Kessel clustering algorithm. The interval Kalman gains in the consequent proposition of interval type-2 fuzzy Kalman filter are updated according to unobservable components computed by recursive spectral decomposition of experimental data. Results illustrate the efficiency of proposed methodology, as compared to other approach widely cited in the literature, for filtering and tracking the state variables of Lorenz’s chaotic attractor in a noisy environment, and its applicability for adaptive and real-time forecasting the dynamic spread behavior of novel coronavirus 2019 (COVID-19) outbreak in state of Maranhão and Brazil.

A Modified Functional Observer-Based EID Estimator for Unknown Continuous-Time Singular Systems

This paper presents the design of a linear quadratic analog tracker (LQAT) based on the observer–Kalman-filter identification (OKID) method and the design of a modified functional observer-based equivalent input disturbance (EID) estimator for unknown square–non-square singular analog systems with unknown input and output disturbances. First, an equivalent mathematical model of the singular analog system is presented to simulate the time response of continuous-time linear singular analog systems to arbitrary inputs via the model conversion method. Then, for the unknown singular analog system, it constructs a linear quadratic analog tracker with state feedback and feed-forward gains based on the off-line OKID method. Furthermore, it extends the design methodology of the EID estimator for strictly proper regular systems with unknown matched–mismatched input and output disturbances to proper regular systems. It is important to mention that the newly developed modified functional observer for proper systems is used to estimate the unknown EID of singular analog systems and that the constraints on the dimensions of unknown disturbances can be eliminated by using the newly proposed EID estimation method. The contributions of this paper can be listed as follows: (1) based on both the OKID method and the discrete-to-continuous model conversion, the simulation of the time responses of the continuous-time linear singular models (which are not feasible using existing MATLAB toolboxes) become feasible; (2) for effective control of the unknown singular analog system, an off-line OKID method is proposed to design an LQAT with state feedback and feed-forward gains; and (3) based on the newly developed modified functional observer for the reduced-order proper regular system, the original EID estimator in the literature is newly extended to estimate the EID from the unknown strictly proper singular analog system, without the original dimensional constraints of the disturbances. It is important to mention that the disturbances of interest can be unknown matched–mismatched input and output disturbances.

Application of the observer/Kalman filter identification method to unknown time-delay disturbed systems and the associated optimal digital tracker design

ABSTRACTMany practical systems are described as unknown multi-input-multi-output (MIMO) time-delay systems with unknown disturbances. The properties and performance of multi-time-delay MIMO systems are quite different compared to delay-free systems, in particular if the time-delay is long. In addition, for practical implementation digital controllers are often required instead of analog controllers. This paper presents: (i) an overview of the mathematical modelling based on the observer/Kalman filter identification (OKID) method, with some insight on known/unknown MIMO systems; (ii) a study of the pole-zero maps of the identified delay-free system and the known/unknown time-delay system for various sampling periods; (iii) a development of the explicit pole-zero map of the sampled-data MIMO neutral system with multiple discrete and disturbed time delays; (iv) an utilisation of the OKID method for known/unknown time-delay sampled-data MIMO systems with unknown disturbances; (v) an extension of the existing equivalent-input-disturbance (EID) estimator, to determine a robust tracker for the unknown time-delay system with unknown disturbances; and (vi) an investigation on the unknown time-delay system with stable or unstable zeros to determine which traditional or customised tracker can be applied. In addition, simulation studies are performed on the relationship between pole-zero maps and delay times.

A modified functional observer-based EID estimator for unknown sampled-data singular systems

This paper presents both an observer/Kalman filter identification (OKID) method-based linear quadratic digital tracker (LQDT) and a new functional observer-based discrete equivalent input disturbance (EID) estimator, for unknown square/non-square singular sampled-data systems with unknown input and output disturbances. Initially, it is shown that even if the solution of the impulsive mode-free singular linear quadratic tracker problem exists, under some quite general conditions the tracker-based generalised algebraic Riccati equation (GARE) might have no solution. To overcome this issue, an innovative methodology that involves an introduced reduced-order equivalent proper regular model (EPRM) of the singular system is presented, to make the tracker-based GARE solvable for a wide class of servo control problems for a singular system. Furthermore, a new functional observer-based design methodology for the discrete EID estimator of the discrete EPRM is proposed in this paper, for a proper sampled-data system with unknown matched/mismatched input and output disturbances. Finally, a discrete-time EPRM of the unknown singular sampled-data system is constructed using the off-line OKID method and the robust prediction-based state-estimate optimal LQDT, associated with the (plug-in) discrete EID estimator, is developed for the singular sampled-data system.

A modified observer/Kalman filter identification (OKID) algorithm employing output residuals

The observer/Kalman filter identification (OKID) is an algorithm widely used for the identification of state space models. The standard OKID algorithm involves the estimation of the Kalman filter and system Markov parameters, followed by the realization of a state space model of the system using the eigensystem realization algorithm (ERA). In this paper, a modified and conceptually simple version of the OKID algorithm, termed the residual-based observer/Kalman filter identification (ROKID), is proposed. The ROKID algorithm uses ordinary least square method twice to solve two linear regression problems yielding the Kalman filter residuals and the system Markov parameters, respectively. Finally, the ERA algorithm is used to obtain a state space model of the system. The efficacy of the proposed algorithm is examined and compared with the standard OKID algorithm and the recently proposed OKID with deterministic projection (OKID/DP) algorithm via a simulation example. The results show that the proposed algorithm outperforms the standard OKID algorithm. Although its performance is less than that of the OKID/DP algorithm, due to its simplicity, the proposed algorithm represents a useful tool for linear state space model identification.

Dynamic modeling and modal parameters identification of satellite with large-scale membrane antenna

With the development of antenna technology, membrane antenna has become a research hotspot in aerospace field due to its advantages of light weight, low cost and easy folding. Nevertheless, greater difficulties have been brought to dynamic modeling and identification of the satellite with membrane antenna since its structure is remarkably flexible and complex. In view of the above problems, in this paper, dynamic modeling and on-orbit parameter identification are investigated for satellite systems with large-scale membrane antennas. Firstly, translation, rotation and vibration dynamic equations of the satellite system are developed using the coupling coefficient method. Afterwards observer/Kalman filter identification (OKID) and eigensystem realization algorithms (ERA) are applied to identify the modal parameters of the system. Finally, the validity of proposed methods are verified by numerical simulations. Simulation results indicate that the dynamic model established by this paper coincides well with the software ADAMS when comparing dynamic responses of the satellite, and also reveal that both OKID and ERA can effectively identify natural frequencies and modes of the system.

Methodology for Evolving Fuzzy Kalman Filter Identification

A methodology based on the smart combination of evolving fuzzy clustering and OKID (Observer/ Kalman Filter Identification) algorithm, is proposed. The evolving fuzzy version of OKID algorithm is formulated for adjusting parameters and structure of the fuzzy Kalman filter, from experimental data. Experimental results from states and outputs estimation applied to online identification of a 2DoF helicopter show the efficiency of the proposed methodology.

Active Vibration Control of the Sting Used in Wind Tunnel: Comparison of Three Control Algorithms

In wind tunnel tests, cantilever stings are often used as model-mount in order to reduce flow interference on experimental data. In this case, however, large-amplitude vibration and low-frequency vibration are easily produced on the system, which indicates the potential hazards of gaining inaccurate data and even damaging the structure. This paper details three algorithms, respectively, Classical PD Algorithm, Artificial Neural Network PID (NNPID), and Linear Quadratic Regulator (LQR) Optimal Control Algorithm, which can realize active vibration control of sting used in wind tunnel. The hardware platform of the first-order vibration damping system based on piezoelectric structure is set up and the real-time control software is designed to verify the feasibility and practicability of the algorithms. While the PD algorithm is the most common method in engineering, the results show that all the algorithms can achieve the purpose of over 80% reduction, and the last two algorithms perform even better. Besides, self-tuning is realized in NNPID, and with the help of the Observer/Kalman Filter Identification (OKID), LQR optimal control algorithm can make the control effort as small as possible. The paper proves the superiority of NNPID and LQR algorithms and can be an available reference for vibration control of wind tunnel system.

Robust observer-based optimal linear quadratic tracker for five-degree-of-freedom sampled-data active magnetic bearing system

ABSTRACTThis paper presents three observer/Kalman filter identification (OKID) approaches and develops a robust observer-based optimal linear quadratic digital tracker (LQDT) for the five-degree-of-freedom (five-DOF) sampled-data active magnetic bearing (AMB) system with various disturbances. The more detailed objectives are: (i) to construct both an equivalent linear time-invariant discrete-time model and its state estimator via the proposed OKID approaches for the AMB system, which might be an unknown nonlinear time-varying unstable system with both a specified rotation speed and a sampling rate; (ii) to provide an adaptive disturbance estimation scheme, which establishes an equivalent input disturbance (EID) estimator for the AMB system with unexpected disturbances; and (iii) to develop a robust observer-based optimal LQDT for the sampled-data AMB system with both a pre-specified time-varying speed and unexpected disturbances. The developed LQDT is able to recover the displacement of the rotor to the pre-specified trajectory position whenever it deviates from such trajectory.