Recursive Identification Research Articles

A New Variable Forgetting Factor-Based Bias-Compensation Algorithm for Recursive Identification of Time-Varying Multi-Input Single-Output Systems With Measurement Noise

This article proposes a new variable forgetting factor (VFF) bias-compensated recursive least-squares (BCRLS) algorithm for the recursive identification of complex time-varying multi-input single-output (MISO) systems with measurement noise. It extends a previously developed real-valued BCRLS algorithm to complex signals and introduces new self-calibrated VFF and noise variance estimation schemes for tracking time-varying systems. The proposed VFF scheme offers faster tracking speed, especially for sudden system changes, while achieving a low steady-state (SS) mean square error (MSE) in a stationary environment. Moreover, the mean and mean square deviation of the complex RLS algorithm under zero-mean white Gaussian output additive noise are performed, from which the variance of the additive noise can be estimated. To mitigate the effect of finite-sample number, a self-calibration scheme is proposed to refine the FF at the SS and hence MSE. Simulations show that the proposed self-calibrated VFF-BCRLS algorithm offers improved tracking speed in sudden system changes and offers smaller MSE over the conventional BCRLS algorithm. Applications to real-world data for pH value prediction of a pH neutralization process and temperature prediction of a glass furnace also demonstrate the effectiveness of the proposed algorithm. The good performance and efficient implementation make it an attractive alternative to other conventional methods for system identification in control and optimization processes and other possible applications.

Optimized dielectric barrier discharge‐plasma actuator for active flow control in wind turbine

The efficiency of horizontal axis wind turbines greatly depends on the efficient utilization of the aerodynamic lift force. The coefficient of lift could be altered using the flow control techniques. The dielectric barrier discharge (DBD)-based plasma actuator is an evolving active flow control technique in which the moment induced in air by DBD plasma activation improves the power capturing capacity of the blades without any mechanical actuation. But due to the offset plasma actuation in extreme wind condition, it would induce structural stress on turbine components. The effect of optimized plasma actuation by varying the voltage amplitude and with a fixed frequency of 24 kHz is to be analyzed. The duty cycle of the plasma actuator is maintained constant at 90%. The optimal point plasma operation would ensure the maximum power production and reduced bending moment of blades. The optimum plasma activation also reduces the power consumption of the actuator. The instantaneous optimum Pareto best is obtained by recursive identification of dynamic system response using non-dominated sorting genetic algorithm 2. The converging points of the algorithm are validated using a NREL FAST 5MW offshore baseline wind turbine model interfaced with MATLAB.

Recursive identification for Wiener non‐linear systems with non‐stationary disturbances

This study investigates the robust recursive identification problem for Wiener non-linear systems with non-stationary disturbance and measurement white Gaussian noise. Non-stationary disturbances cannot be eliminated by conventional statistical strategy. To overcome such problem, the non-stationary disturbance signal is modelled as a dynamic parameter with a small change rate which is to be estimated step. Utilising the forgetting factor (FF) and the auxiliary model strategy, a discrete-time recursive least-squares algorithm is designed by augmenting the parameter vector and the information vector. To facilitate the steady asymptotic convergence of the time-invariant system parameters and the dynamic tracking ability of the disturbance, two adaptive FFs are proposed to construct a new matrix FF scheme that is used to update the covariance matrix. Moreover, several asymptotic convergence conditions are also derived based on the stochastic statistical theory under persistent excitation condition. Finally, one illustrative example with non-stationary disturbance is employed to show the effectiveness and advantages of the proposed algorithms.

Developing data fusion and recursive estimation methods for online identification of dive plane dynamics of an autonomous underwater vehicle

The purpose of this article is to develop an online method to identify the hydrodynamic coefficients of pitch plane of an autonomous underwater vehicle. To obtain necessary data for the identification, the dive plane dynamics should be excited through diving maneuvers. Hence, a controller is needed whose performance and stability are appropriate. To design such a controller, first, hydrodynamic coefficients are approximated using semi-empirical methods. Based on these approximated coefficients, a classic controller is designed at the next step. Since the estimation of these coefficients is uncertain, µ-analysis is employed to verify the robustness of stability and performance of the controller. Using the verified robust controller, some oscillating maneuvers are carried out that excite the dive plane dynamics. Using sensor fusion and unscented Kalman filter, smooth and high-rate data of depth is provided for the depth controller. A recursive identification algorithm is developed to identify the hydrodynamic coefficients of heave and pitch motions. It turns out that some inputs required by the identification are not measured directly by the sensors. But the devised fusion algorithm is able to provide the necessary data for identification. Finally, using the identified coefficients and employing pole placement method, a new controller with better performance is synthesized online. To evaluate the performance of the identification and fusion algorithms, a 6-degree-of-freedom simulation of an autonomous underwater vehicle is carried out.

Comparative Analysis of Identification Methods for Mechanical Dynamics of Large-Scale Wind Turbine

With increasing size and flexibility of modern grid-connected wind turbines, advanced control algorithms are urgently needed, especially for multi-degree-of-freedom control of blade pitches and sizable rotor. However, complex dynamics of wind turbines are difficult to be modeled in a simplified state-space form for advanced control design considering stability. In this paper, grey-box parameter identification of critical mechanical models is systematically studied without excitation experiment, and applicabilities of different methods are compared from views of control design. Firstly, through mechanism analysis, the Hammerstein structure is adopted for mechanical-side modeling of wind turbines. Under closed-loop control across the whole wind speed range, structural identifiability of the drive-train model is analyzed in qualitation. Then, mutual information calculation among identified variables is used to quantitatively reveal the relationship between identification accuracy and variables’ relevance. Then, the methods such as subspace identification, recursive least square identification and optimal identification are compared for a two-mass model and tower model. At last, through the high-fidelity simulation demo of a 2 MW wind turbine in the GH Bladed software, multivariable datasets are produced for studying. The results show that the Hammerstein structure is effective for simplify the modeling process where closed-loop identification of a two-mass model without excitation experiment is feasible. Meanwhile, it is found that variables’ relevance has obvious influence on identification accuracy where mutual information is a good indicator. Higher mutual information often yields better accuracy. Additionally, three identification methods have diverse performance levels, showing their application potentials for different control design algorithms. In contrast, grey-box optimal parameter identification is the most promising for advanced control design considering stability, although its simplified representation of complex mechanical dynamics needs additional dynamic compensation which will be studied in future.

Stochastic and recursive estimation of the hygro-thermo-chemical-mechanical parameters of concrete through Monte Carlo analysis and extended Kalman filter

Hygro-thermo-chemical-mechanical models, used to determine the variations over time of temperature, relative humidity and shrinkage induced deformations in concrete components, are characterised by the presence of a large number of input parameters. Some of these parameters can be evaluated on the basis of the concrete mix specifications or from literature data, while the others present a large variability and, in some cases, do not have a precise physical meaning and, for this reason, require the implementation of proper identification strategies. The experimental work involved for this characterisation can be time-consuming and costly because based on the long-term monitoring of the time evolution of the field quantities in specific positions within concrete components. The aim of this paper is to propose and validate recursive identification strategies that exploit, in a step by step fashion, the information coming from the experimentation for the identification of the model input parameters. The influence of different exposure conditions and of different concrete thicknesses are investigated and, for each scenario considered, the expected identification error of each parameter is estimated, within a stochastic context implemented through Monte Carlo analyses and Kalman Filter, as a function of the monitored time.

Recursive Identification of Quantized Linear Systems

This paper studies the identification of linear systems with quantized output observations. Recursive estimates for the linear system and the quantization thresholds are derived by the stochastic approximation algorithms with expanding truncations (SAAWET). Under suitable conditions, it is shown that the estimates converge to the true values almost surely.

Recursive Identification Algorithms for a Class of Linear Closed-loop Systems

This paper focuses on the identification problems for a class of linear closed-loop systems. On one hand, the identifiability condition is investigated for the case where the controller is in series with the plant on the forward channel. On the other hand, the identification model is derived after parametrization, in which the parameter vector only contains the parameters of the controlled plant instead of the whole closed-loop system, and a recursive least squares algorithm and a stochastic gradient algorithm are proposed for closed-loop systems. In order to improve the parameter estimation accuracy, a forgetting factor and a convergence index are introduced into the proposed stochastic gradient algorithm. The simulation results demonstrate the effectiveness of the proposed algorithms.

Particle filtering‐based recursive identification for controlled auto‐regressive systems with quantised output

Recursive prediction error method is one of the main tools for analysis of controlled auto-regressive systems with quantised output. In this study, a recursive identification algorithm is proposed based on the auxiliary model principle by modifying the standard stochastic gradient algorithm. To improve the convergence performance of the algorithm, a particle filtering technique, which approximates the posterior probability density function with a weighted set of discrete random sampling points is utilised to correct the linear output estimates. It can exclude those invalid particles according to their corresponding weights. The performance of the particle filtering technique-based algorithm is much better than that of the auxiliary model-based one. Finally, results are verified by examples from simulation and engineering.

Recursive Kronecker-Based Vector Autoregressive Identification for Large-Scale Adaptive Optics

This brief presents an algorithm for the recursive identification of Vector AutoRegressive (VAR) models of large dimensions. We consider a VAR model where the coefficient matrices can be written as a sum of Kronecker products. The algorithm proposed consists of recursively updating the Kronecker factor matrices at each new time step using alternating least squares. When the number of terms in the Kronecker sum is small, a significant reduction in computational complexity is achieved with respect to the recursive least squares algorithm on an unstructured VAR model. Numerical validation of nonstationary atmospheric turbulence data, both synthetic and experimental, is shown for an adaptive optics application. Significant improvements in accuracy over batch identification methods that assume stationarity are observed while both the computational complexity and the required storage are reduced.

Entrepreneurshp at the labour market: a case of precariat and informal employment

The concept of precariat is becoming the increasingly important subject of interdisciplinary research that involves both qualitative and quantitative approaches. The formation of the precariat is associated with the neoliberal reforms carried out in the last decades, as well as significant institutional and technological changes. The process of precarisation is accompanied by an increase in insecurity, instability, and flexibility, which is most characteristic of informal and precarious work. Our paper analyzes the relationship between informal employment as a proxy precariat and unemployment rates, industrial production index and real wages using the structural VAR approach for monthly data in the period 2010-2018. The relationship between the variables is checked by imposing restrictions on the recursive scheme (Cholesky identification) as well as the recursive identification scheme (Cholesky decomposition) in the SVAR model. Our analysis of the impulse response caused by the positive shock of informal employment confirmed that in the short term, the increase in the share of people employed in the informal sector causes, above all, a decline in real wages. There are weak responses from the industrial production index, which leads to the conclusion about the leveling effect of institutions and institutions. In addition, the paper employs the process of modeling the development of informal employment using the ARIMA model. Our results showing the trends in the development of informal employment demonstrate the existence of cyclical resilience which negatively affects economic development and requires structural reforms.

The Mechanisms of Radix Bupleuri-Paeonia lactiflora in the Treatment of Depresive Disorder Predicted by Network Pharmacology

Designing a fully automated artificial pancreas (AP) system is challenging. Changes in the glucose-insulin dynamics in the human body over time, and the inter-subject and day-to-day variability of people with type 1 diabetes (T1D) are two important factors that would highly undermine the performance of an AP that is based on time-invariant and non-individualized models. People with T1D show different responses to carbohydrate intake, insulin, physical activity and stress with day-to-day variability present between or within specific patients. Thus, the control law in an AP system requires a reliable time-varying individualized model to perform efficiently. In this work, a novel recursive identification approach called a Predictor-Based Subspace Identification (PBSID) method is used for identifying a linear time-varying glucose-insulin model for each individual. Model identification and validation are based on clinical data from closed-loop experiments. The models are evaluated by means of various performances indices: Variance Accounted For (VAF), Root mean square error (RMSE), Normalized root mean square error (NRMSE) and Normalized mean square error (NMSE). The proposed method provides a stable time-varying state space model over time. It can be also individualized for each patient by defining the order of the system correctly. The approach proposed in this work has shown a strong potential to identify a consistent glucose-insulin model in real time for use in an AP system.

Recursive identification of block-oriented nonlinear systems in the presence of outliers

The paper considers the recursive identification of nonlinear (Hammerstein) model in the presence of outliers. In this model the nonlinear part is a polynomial of a known order in the input and linear part is described as an ARX (auto - regressive model with exogenous inputs) model. It is assumed that there is a priori information about a disturbance distribution in the form of a class of distributions. Owing that fact it is possible to use robust statistics in the sense of Huber. But Huber`s loss function is only first order differentiable. It follows that second order methods (Newton – Raphson methodology) cannot be used. The problem is avoided by analysis of the structure of least favourable distribution. It is shown that robust recursive algorithm derivation can be set in frame of l1−l2 – norm estimation problem. The main contributions of the paper are: (i) it is shown that the robust identification belongs to l1−l2 – norm estimation problem; (ii) the derivation of the new robust recursive algorithm; (iii) it is shown that robust recursive algorithm is switching algorithm (collection of linear least squares and sign algorithm) and that fact opens the new research opportunities.

Which oil shocks really matter in equity markets?

This paper examines the relationship between structural oil shocks and US equity markets. The recent oil shock decomposition of Ready (2018) is reconsidered and refined, providing a clearer delineation between shocks to equity market discount rates and aggregate demand, leading to an oil shock specification which attributes substantially more explanatory power to the latter in explaining equity market variation. Providing links with the literature dating back to Kilian and Park (2009), an explicit role is given to precautionary demand shocks using an independent measure constructed from oil futures data, reducing the role of the supply shocks obtained as the final residual in the recursive identification scheme. In an extended sample that allows an analysis of the oil/equity market relationship since the global financial crisis, the modified aggregate demand shocks have approximately twice as much explanatory power for stock return variation than the demand shocks of Ready (2018). The importance of these shocks in driving oil price changes and equity market volatility has only increased since the financial crisis, with the role of supply shocks diminishing. Once these demand effects are accounted for, there is little relationship between precautionary demand shocks and equity returns, in contrast to the existing literature.

Long-term robust identification potential of a wavelet packet decomposition based recursive drift correction of E-nose data for Chinese spirits

The drift of electronic nose (E-nose) is always yielded, and makes it does not possess long-term robust detection ability, so that the detection accuracy of the same samples tested in the subsequent period will be reduced. In order to enhance the long-term identification robustness of six kinds of Chinese spirits, a recursive identification model was established. Firstly, E-nose data were decomposed by a wavelet packet and generated decomposition coefficients. Then a relative deviation threshold function was constructed to handle these coefficients. And then, the E-nose data with little drift or not were obtained by reconstructing the corrected coefficients. Finally, a concept of “sample test time window” (SMTW) was introduced for building the recursive identification model. The six kinds of spirit samples were discontinuously tested for 16 months, and the SMTW was determined as 6 months. As SMTW moves forward for 2 months every time, the recursive identification model based on Fisher discriminant analysis (FDA) was also built and the correct identification rate was 96.5%, namely the tested samples in 2 months of following SMTW could be accurately identified. This illustrates that the proposed methods are very effective.

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.

Recursive identification for Hammerstein systems with diminishing excitation signals

In this paper, we consider the identification of Hammerstein systems where the nonlinearity is described by a combination of basis functions with unknown coefficients. The extended least squares (ELS) algorithm is applied to estimate the unknown parameters in the system. Contrary to the classical excitation signals for identification of Hammerstein systems, i.e., the periodic inputs or stationary random signals, here we choose a sequence of diminishing excitation signals as the system inputs. We prove that the strong consistency of the ELS algorithm still holds true and the convergence rate is obtained as well. A numerical example is given to verify the performance of the identification method.

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.