Recursive Identification Method Research Articles

Robust Recursive Identification of ARX Models Using Beta Divergence

The robust recursive identification method of ARX models is proposed using the beta divergence. The proposed parameter update law suppresses the effect of outliers using a weight function that is automatically determined by minimizing the beta divergence. A numerical example illustrates the efficacy of the proposed method.

The Online Identification of the Behaviour of Pollutants inside the Tunnel Tube

A tunnel tube is a relatively small space that allows for the accumulation of gaseous and liquid substances containing harmful substances. Given this fact, a ventilation system is the most critical component of a tunnel’s technological equipment, greatly influencing its reliability and safe operation. The dynamic behaviour of pollutants in the tunnel tube is characterized by a significant stochastic component and changing parameters over time due to pressure, airflow, and atmospheric condition changes. This work addresses the issue of modelling individual parts of the tunnel tube for optimal tunnel ventilation control. It is necessary to create a model of a controlled system that is used for predicting process variables to calculate optimal control action. By using recursive identification methods in conjunction with a predictive controller, the proposed concept can be applied to numerous similar applications.

Parametric Modeling and Deep Learning for Enhancing Pain Assessment in Postanesthesia.

The problem of reliable and widely accepted measures of pain is still open. It follows the objective of this work as pain estimation through post-surgical trauma modeling and classification, to increase the needed reliability compared to measurements only. This article proposes (i) a recursive identification method to obtain the frequency response and parameterization using fractional-order impedance models (FOIM), and (ii) deep learning with convolutional neural networks (CNN) classification algorithms using time-frequency data and spectrograms. The skin impedance measurements were conducted on 12 patients throughout the postanesthesia care in a proof-of-concept clinical trial. Recursive least-squares system identification was performed using a genetic algorithm for initializing the parametric model. The online parameter estimates were compared to the self-reported level by the Numeric Rating Scale (NRS) for analysis and validation of the results. Alternatively, the inputs to CNNs were the spectrograms extracted from the time-frequency dataset, being pre-labeled in four intensities classes of pain during offline and online training with the NRS. The tendency of nociception could be predicted by monitoring the changes in the FOIM parameters' values or by retraining online the network. Moreover, the tissue heterogeneity, assumed during nociception, could follow the NRS trends. The online predictions of retrained CNN have more specific trends to NRS than pain predicted by the offline population-trained CNN. We propose tailored online identification and deep learning for artefact corrupted environment. The results indicate estimations with the potential to avoid over-dosing due to the objectivity of the information. Models and artificial intelligence (AI) allow objective and personalized nociception-antinociception prediction in the patient safety era for the design and evaluation of closed-loop analgesia controllers.

Auxiliary model‐based interval‐varying maximum likelihood estimation for nonlinear systems with missing data

AbstractThe identification problem of nonlinear system with missing data is focused in this article. In order to overcome the system unavailable outputs, an auxiliary model‐based interval‐varying recursive identification method is derived by changing the sampling interval and substituting the missing output with the output of an auxiliary model. Based on the maximum likelihood principle and the least‐squares method, a maximum likelihood‐based interval‐varying recursive least‐squares method is investigated. The validity of the proposed maximum likelihood method is tested by a numerical simulation example and a practical continuous stirred tank reactor (CSTR) process.

Modal Parameter Identification of Recursive Stochastic Subspace Method

In bridge health monitoring, in order to closely monitor the structural state changes of the bridge under heavy traffic load and other harsh environments, the monitoring system is required to give the change process of structural modal parameters. Due to the symmetric variables of bridge monitoring during operation, the evaluation needs to be completed by the recursive identification of modal parameters based on environmental excitation, especially the recursive recognition of the random subspace method with high recognition accuracy. We have studied the recursive identification methods of covariance-driven and data-driven random subspace categories respectively, established the corresponding recursive format, and used the model structure of the ASCE structural health monitoring benchmark problem as a numerical example to verify the reliability of the proposed method. First, based on the similar interference environment of the observation data at the same time, a reference point covariance-driven random subspace recursive algorithm (IV-RSSI/Cov) based on the auxiliary variable projection approximation tracking (IV-PAST) algorithm is established. The recursive format of the system matrix and modal parameters is obtained. Based on Givens rotation, the rank-2 update form of the row space projection matrix is established, and the recursive format of the data-driven recursive random subspace method (RSSI/Data) under the PAST algorithm is obtained. Then, based on the benchmark problem of ASCE-SHM, the response of the model structure under environmental excitation is numerically simulated, the frequency, damping ratio and vibration mode of the structure are recursively tracked, and their reliability and shortcomings are studied. After improving the recursive method, the frequency tracking accuracy has been improved, with a maximum accuracy of 99.8%.

Dynamic force identification in milling based on IRLS using acceleration signals

Measurement of cutting force is important for in-process monitoring, control and optimization. However, it is very difficult to measure the cutting force directly using invasive sensor in industrial scene. This paper develops an infinite-time recursive identification method of cutting force under finite buffer length condition, called the improved recursive least squares (IRLS) method. A cutting force identification framework based on time-domain convolutional theory is introduced, where the cutting force is identified using the acceleration signal easily obtained from industrial scene. Then, the decay characteristic of the impulse response function and the recursive characteristic of the transfer matrix are used to improve the recursive least squares method. The IRLS method overcomes the data saturation problem of the recursive least squares method and can identify the cutting force in infinite time. To reduce the error amplification of the proposed cutting force identification method, the averaged transfer function is used to determine the length of the buffer. In addition, the compensated values of the Kistler 9129AA dynamometer measurement results are used as a reference. Finally, several sets of milling experiments are performed to verify the effectiveness and rationality of the IRLS method.

Joint two‐stage multi‐innovation recursive least squares parameter and fractional‐order estimation algorithm for the fractional‐order input nonlinear output‐error autoregressive model

SummaryThis paper mainly investigates the issue of parameter identification for the fractional‐order input nonlinear output error autoregressive (IN‐OEAR) model. In order to avoid the problem of large computation of redundant parameter estimation, the output form of the system can be expressed by a linear combination of unknown parameters through the key term separation. Through employing the hierarchial identification principle, the fractional‐order IN‐OEAR model is decomposed into two sub‐models with a smaller number of parameters. On the basis of the recursive identification methods, a recursive least squares sub‐algorithm and a gradient stochastic sub‐algorithm are proposed to estimate the parameters and the fractional‐order, respectively. With the aim of achieving more accurate parameter estimates, a two‐stage multi‐innovation least recursive algorithm is proposed by means of the multi‐innovation identification theory. The numerical simulation results test the effectiveness of the proposed methods.

Research on Adaptive Prescribed Performance Control Method Based on Online Aerodynamics Identification

Wide-speed-range vehicles are characterized by high flight altitude and high speed, with significant changes in the flight environment. Due to the strong uncertainty of its aerodynamic characteristics, higher requirements are imposed on attitude control. In this paper, an adaptive prescribed performance control method based on online aerodynamic identification is proposed, which consists of two parts: an online aerodynamic parameter identification method and an adaptive attitude control method based on the pre-defined parameters of the control system. The aerodynamic parameter identification is divided into offline design and online design. In the offline design, neural networks are used to fit nonlinear aerodynamic characteristics. In the online design, a nonlinear recursive identification method is used to correct the errors of the offline fitted model. The adaptive attitude control is based on the conventional control method and updates the control gain in real time according to the desired system parameters to enhance the robustness of the controller. Finally, the effectiveness of the offline neural network and online discrimination correction is verified by mathematical simulations, and the effectiveness and robustness of the adaptive control proposed in this paper are verified by comparative simulation.

Vintage article: the effect of monetary policy shocks in the UK: an external instruments approach

AbstractThis paper uses vector autoregression model analysis to identify monetary policy shocks on UK data using surprise changes in the policy rate as external instruments and imposing block exogeneity restrictions on domestic variables to estimate parameters from the viewpoint of the domestic economy. The results show large and persistent effects of monetary policy shocks on the domestic economy and point to the critical role of exchange rates and term premia. The analysis resolves important empirical puzzles of traditional recursive identification methods.

A novel multi-innovation gradient support vector machine regression method

For the regression problem of support vector machine, the solution processes of the most existing methods use offline datasets, which cannot be realized online. For this problem, this paper presents a new online approach to identify these unknown parameters contained in the support vector machine. A new cost function is constructed by substituting the error term into the standard cost function, which is different from the standard support vector machine, and the gradient descent approach is then used to minimize the newly created loss function, thus proposing a stochastic gradient support vector machine algorithm to estimate the unknown parameters based on the recursive identification methods. Furthermore, to advance the property of the stochastic gradient support vector machine algorithm, a moving data window is used to widen the scalar information into a fixed-length innovation vector, thereby increasing the amount of information used in the parameter estimation based on the multi-innovation identification theory. In addition, the forgetting factor is brought into the proposed algorithms, and the corresponding forgetting factor recursive algorithms are derived. These methods are recursive identification methods, which may be implemented online and are more efficient in terms of computing. Finally, utilizing the MatLab platform, the validity and usefulness of the explored methodologies are proven using several numerical simulation examples.

Filtering‐based multi‐innovation recursive identification methods for input nonlinear systems with piecewise‐linear nonlinearity based on the optimization criterion

AbstractPiecewise‐linear nonlinearity is an effective representation for hard nonlinearities such as saturation, dead zone, and backlash, which can be also used as a general tool for approximating nonlinear characteristics. For the input piecewise‐linear output‐error autoregressive systems, we develop a parametric expression of the piecewise‐linear nonlinearity through a switching function and position functions, and derive the identification model of the system by using the key item separation. Based on the optimization criterion, an auxiliary model‐based multi‐innovation recursive generalized least‐squares algorithm is deduced for estimating the unknown parameters according to the obtained model. Since the system is disturbed by colored noise, we introduce the data filtering technique from a view point of improving the parameter estimation accuracy. The filtering identification model of the system is derived and a filtering‐based multi‐innovation recursive generalized least‐squares algorithm is proposed. The simulation example demonstrates the effectiveness of the proposed algorithms and shows that the filtering‐based multi‐innovation recursive generalized least‐squares algorithm has better identification performance.

An efficient recursive identification algorithm for multilinear systems based on tensor decomposition

AbstractThere are many important fields involving the multilinear system identification. A great number of parameters to be identified is an important challenge, leading to the need for tensorial decomposition and modeling of such systems. This article is about the parameter estimation of the higher‐order multilinear systems with non‐Gaussian noises and to explore the role of tensor algebra in the multilinear model identification. A high‐dimension system identification problem is reformulated in terms of low‐dimension problems by using the tensorial decomposition technique. Further, applying the multi‐innovation identification theory, the recursive algorithm combining with the logarithmic p‐norms is investigated for multilinear systems with non‐Gaussian noises of low computational complexity. Finally, some simulation results illustrate the effectiveness of the proposed recursive identification method.

Multi‐innovation Newton recursive methods for solving the support vector machine regression problems

AbstractThe support vector machine has been widely used in binary classification applications because of the simplicity of its implementation. This article proposes an online identification method based on the support vector machine in the field of parameter identification. By substituting the constraint item into the original criterion function to form a new criterion function about the weight vector and the bias item, and then on the basis of the recursive identification methods, the newly established criterion function is minimized by using the Newton search to derive the Newton recursive support vector machine algorithm. Additionally, in order to improve the performance of the Newton recursive support vector machine algorithm, the multi‐innovation identification theory is applied to optimize the algorithm, and a multi‐innovation Newton recursive support vector machine algorithm is derived. In addition, the convergence and the calculation amount of the proposed algorithms are carefully analyzed in this article. Finally, a numerical simulation example is given to compare the Newton recursive algorithm and the corresponding multi‐innovation recursive algorithm. The results show that the algorithms and optimization strategy studied in this article are effective.

Adaptive sliding mode control with information concentration estimator for a robot arm

ABSTRACTThere are nonlinear disturbances in actual systems, and all kinds of nonlinear disturbances may make the performances of actual systems become worse, besides, sometimes it is difficult to obtain a simplified model of the actual system owing to complex production technologies and processes. The existence of both two kinds of uncertainties makes it difficult to directly apply traditional recursive identification methods based on parametric systems. In this paper, first, an improved information concentration (IC) estimator is introduced for estimating unknown parameters of parametric uncertainty part by using historical data, and an adaptive sliding mode controller based on the proposed IC estimator is investigated for the speed control system of a robot arm. Second, the stability of adaptive sliding mode control based on the proposed IC estimator for the speed control system of a robot arm is analysed. Finally, two simulation examples are carried out. The experimental results indicate that the proposed IC estimator is effective in estimating unknown parameters.

Novel adaptive methods for output-only recursive identification of time-varying systems subject to gross errors

Gross errors are generally used to model intermittent sensor failures and occasional data packet losses or corruption, which arise in many engineering communities. In this work, we propose to deal with the problem of output-only recursive identification of time-varying systems subject to gross errors by using an adaptive weighting and forgetting combined strategy. Under the assumption that gross errors are unknown and can be of arbitrarily large magnitude, time-dependent autoregressive model-based adaptive recursive identification methods are proposed by minimizing the sum of norm errors and achieving a sparse prediction error sequence. The adaptive weighting strategy is used to deemphasize data observations contaminated by gross errors, and the forgetting mechanism is used to deemphasize data from the remote past, allowing the proposed methods to track time-varying dynamics of the system subject to gross errors. The proposed methods are numerically and experimentally tested, and the comparative results demonstrate the superior time-varying tracking capability of the proposed methods in extremely challenging gross error circumstances.

Fractional-Order Modeling and Identification for a Phantom EEG System

This paper is about dynamical modeling of an electroencephalographic (EEG) measurement chain. It is based on a home-made experimental setup consisting of an electrolytic medium, stimulated by external electrodes, the activity of which is measured at different points via other electrodes, connected to an EEG recording device. A novel noninteger-order model structure is then established with a so-called constant phase element, and a Nyquist-based graphical method is derived to identify the noninteger order. The study is completed with a recursive identification method for full parameter estimation in the model, and various applications on experimental data are presented, finally resulting in a fully identified noninteger order high-pass filter.

Monitoring and Identification of Vibration Frequencies on a Portion of México City Metro Line 12

The use of recursive subspace‐based identification methods is analyzed in the estimation of the most significant vibration frequencies along an elevated railroad segment of México City Metro Line 12 using ambient vibration measurements recorded from 2012, when the line was opened, to 2018. Due to the railroad characteristics, the use of high‐order models and the systematic tuning of the methods are required to achieve low uncertainty in frequency estimation. A frequency history is generated using these high‐order models in order to check for variations along the seven years where important events took place: two low‐ and one high‐intensity earthquakes, paving, and construction of sidewalks and planters around the sensor station. Results are consistent for all methods under analysis in the identified frequencies, suggesting that the system has preserved its structural health. To produce independent results, spectral analysis was performed showing that the associated frequency history is again consistent with that generated with recursive subspace‐based identification methods. Overall, results indicate that these subspace methods are suitable for frequency monitoring in the studied system offering, in the case of recursive N4SID, important advantages in terms of low computational cost, real‐time implementation, and smaller uncertainty.

Continuous identification for mechanistic force models in milling

Force determines the product quality, the productivity and the safety of a milling process. Mechanistic force models are the key to understand, optimize or control the cutting process. They combine the undeformed chip parameter with empiric tuning coefficients in a gray-box model. Identifying those coefficients is costly in both, time and number of experiments. This paper introduces two recursive identification methods for force model identification: recursive least squares and ensemble Kalman filters. The model is nonlinear. The ensemble Kalman filter shows an extraordinary robustness against measurement noise and a fast convergence time -depending on the selection of the ensemble size and the measurement noise. The recursive least squares fit serves as a benchmark but is highly sensitive to measurement noise. It is the first time that a continuous identification is examined for mechanistic force models in milling.

Switch detection and robust parameter estimation for slowly switched Hammerstein systems

Switch detection and robust identification for slowly switched Hammerstein systems are considered in this paper. The switching law is slow, arbitrary and cannot be observed online. A two-identifier-based switch detection scheme is proposed, in order to achieve fast adaptability and robustness of parameter estimation. Specifically, at first, a recursive identification method based on long-horizon iteration is exploited under impulsive noise, and its convergence for time-invariant systems is verified. Secondly, to follow the changes of real processes, a forgetting factor is introduced, and two recursive identifiers with different horizon lengths are developed. Identifier (I) with the long horizon length can resist the influence of outliers, and Identifier (II) is responsible for process rapid reactions. Then, the estimated difference between two identifiers is analyzed to distinguish possible switching points from impulsive noise. Consequently, the two-identifier-based switch detection scheme is formed. Finally, a simulation example demonstrates the effectiveness of the proposed scheme.

Recursive generalized extended least squares and RML algorithms for identification of bilinear systems with ARMA noise

Bilinear systems are considered as a particular class of nonlinear systems including the state variables which are typically used for online identification. By using a recursive identification method and the maximum likelihood principle, this paper presents two recursive-based algorithms to identify the parameters of bilinear in parameter systems with ARMA noise. In this regard, recursive generalized extended least squares (RGELS) and recursive Maximum Likelihood (RML) algorithms have been proposed for identification of bilinear systems. These algorithms can be used as an alternative choice in system identification with acceptable performance. The proposed algorithms estimate the correlated noise parameters with high accuracy by making full use of the measurement data. Simulation results indicate that the proposed algorithms are effective for online identification of bilinear in parameter systems with high convergence speed.