Recursive Identification Algorithm Research Articles

Selection of Sustainable Process and Essential Indicators for Decision Making Using Machine Learning Algorithms

Sustainability of processes or systems is generally evaluated with metrics or indicators. When a set of indicators is identified for a particular system of study, it is important to ensure that all the indicators are necessary and sufficient in defining system sustainability. The indicators should be able to distinguish sustainable process options from unsustainable ones. Generally, a large number of indicators are used to characterize a system. While some of the indicators are essential sustainable indicators, they may not be relevant in defining the particular system of interest. It is essential to select the most important indicators from a large set so that reduced set of indicators can enhance the generalized performance of sustainable process selection algorithm. In this paper, we propose the use of machine learning algorithms including k-means clustering for sustainable process selection and support vector machine recursive feature elimination algorithm (SVM-RFE) for relevant indicator identification that is important in sustainable process classification from a group of competing process options. The method is based on weight vector derivatives or generalized error bound sensitivity with respect to each indicator. The proposed method of relevant indicator selection is compared with previous work on important indicator identification using partial least square-variable importance in projection (PLS-VIP) method. We have used two case studies to demonstrate the methodologies. While the PLS-VIP method was successful in identifying indicators that are sufficient for finding relative importance of different process options, SVM-RFE method is useful for identifying indicators that are sufficient in sustainable process classification.

Laguerre based predictors in discrete-time recursive algorithms: A solution for open-loop identification under oversampling

In this paper we propose a novel formulation of the predictor used in open-loop recursive identification algorithms. The predicted output is expressed by means of an orthogonal Laguerre transfer functions basis. This predictor representation presents many advantages: It makes it possible to identify robustly oversampled systems without any bias in low frequency, and to obtain relevant reduced order models. The Laguerre pole plays the role of a tuning parameter enabling the selection of the best approximation frequency area. The proposed schemes address both output error and ARMAX systems. Simulation and experimental results show all the practical benefits provided by these algorithms.

Unknown Offset Free MPC for Buck Converter

Buck converters are commonly used as DC power supplies. To deal with the parameters uncertainty in R-L (resistance-inductance), an Unknown Offset Free Model Predictive Control (UOFMPC) method for buck converters have been proposed in this paper. Firstly, a continuous model for buck converters is established. Based on it, a discrete model with fixed sampling time is derived and the output of controller is set as the direct switch on/off signals. Secondly, one-step MPC method aimed at optimizing the output voltage with recursive least squares algorithm for parameters identification is given to satisfy the ability of adaptation in parameters. Finally, both the model and control scheme are validated by simulation in MATLAB/Simulink.

Fuzzy Adaptive Decentralized Optimal Control for Strict Feedback Nonlinear Large-Scale Systems.

This paper considers the optimal decentralized fuzzy adaptive control design problem for a class of interconnected large-scale nonlinear systems in strict feedback form and with unknown nonlinear functions. The fuzzy logic systems are introduced to learn the unknown dynamics and cost functions, respectively, and a state estimator is developed. By applying the state estimator and the backstepping recursive design algorithm, a decentralized feedforward controller is established. By using the backstepping decentralized feedforward control scheme, the considered interconnected large-scale nonlinear system in strict feedback form is changed into an equivalent affine large-scale nonlinear system. Subsequently, an optimal decentralized fuzzy adaptive control scheme is constructed. The whole optimal decentralized fuzzy adaptive controller is composed of a decentralized feedforward control and an optimal decentralized control. It is proved that the developed optimal decentralized controller can ensure that all the variables of the control system are uniformly ultimately bounded, and the cost functions are the smallest. Two simulation examples are provided to illustrate the validity of the developed optimal decentralized fuzzy adaptive control scheme.

Identification of Discrete-Time Output Error Model Using Filtered Input Excitation for Integrating Processes With Time Delay

A discrete-time output error (OE) model identification method is proposed for industrial integrating processes with time delay, to facilitate the discrete-time controller design and implementation in sampled systems. By subtly introducing a differential filter to the input excitation, an open-loop identification test can be performed for such a process while complying with the output limit. Correspondingly, the parameter estimation is equivalently transformed to identify a stable type OE model with time delay. A recursive identification algorithm is developed to simultaneously estimate all the model parameters including the integer delay, and a linear interpolation of the input excitation is given for the recursive computation to guarantee consistent estimation. The convergence of parameter estimation is analyzed with a proof. An illustrative example is used to demonstrate the effectiveness of the proposed method.

Stabilization by forwarding design for switched feedforward systems with unstable modes

SummaryThe problem of global stabilization is investigated for a class of switched nonlinear feedforward systems in this paper where the solvability of the stabilization problem for individual subsystem is not assumed. Some sufficient condition for the stabilization problem to be solvable is derived for the first time by exploiting the multiple Lyapunov functions method and the forwarding technique. Also, we design a switching law and construct bounded state feedback controllers of subsystems explicitly by a recursive design algorithm to achieve global asymptotic stability. The provided technique permits removal of a common restriction in which all subsystems in switched nonlinear feedforward systems are globally asymptotically stable. Finally, a numerical example is provided to demonstrate the feasibility of the theoretical result. Copyright © 2017 John Wiley & Sons, Ltd.

Recursive identification of Hammerstein systems with dead-zone nonlinearity in the presence of bounded noise

ABSTRACTThe existing identification algorithms for Hammerstein systems with dead-zone nonlinearity are restricted by the noise-free condition or the stochastic noise assumption. Inspired by the practical bounded noise assumption, an improved recursive identification algorithm for Hammerstein systems with dead-zone nonlinearity is proposed. Based on the system parametric model, the algorithm is derived by minimising the feasible parameter membership set. The convergence conditions are analysed, and the adaptive weighting factor and the adaptive covariance matrix are introduced to improve the convergence. The validity of this algorithm is demonstrated by two numerical examples, including a practical DC motor case.

Recursive Subspace Identification Algorithm using the Propagator Based Method

<p>Subspace model identification (SMI) method is the effective method in identifying dynamic state space linear multivariable systems and it can be obtained directly from the input and output data. Basically, subspace identifications are based on algorithms from numerical algebras which are the QR decomposition and Singular Value Decomposition (SVD). In industrial applications, it is essential to have online recursive subspace algorithms for model identification where the parameters can vary in time. However, because of the SVD computational complexity that involved in the algorithm, the classical SMI algorithms are not suitable for online application. Hence, it is essential to discover the alternative algorithms in order to apply the concept of subspace identification recursively. In this paper, the recursive subspace identification algorithm based on the propagator method which avoids the SVD computation is proposed. The output from Numerical Subspace State Space System Identification (N4SID) and Multivariable Output Error State Space (MOESP) methods are also included in this paper.</p>

A Self-Sensing Approach for Dielectric Elastomer Actuators Based on Online Estimation Algorithms

This paper develops a position self-sensing approach for a motion actuator based on a dielectric elastomer membrane. The proposed method uses voltage and current measurements to estimate the electrical resistance and capacitance online by means of a high-frequency low-amplitude voltage component injected in the actuation signal. The actual deformation is subsequently reconstructed using a model-based estimate of the electrical parameters implemented on a field programmable gate array platform (FPGA) with a sampling frequency of 20 kHz. The main peculiarity of the approach is the use of recursive identification and filtering algorithms that avoid the need of charge measurements. The self-sensing algorithm is extensively validated on a precision linear-motion actuator, which uses a nonlinear biasing system to obtain large actuation strokes.

Generalized 3-D Constellation Design for Spatial Modulation

Spatial modulation (SM) conveys information bits by utilizing both the antenna index and complex symbols to form a 3-D constellation. Similar to 2-D modulation, the structure of 3-D constellation could greatly affect the transmission reliability. In this paper, a generalized 3-D constellation design is proposed to optimize the constellation diagram used for each antenna, i.e., to optimize the complex symbols and their total number for each antenna and finally to enhance the transmission reliability. The optimal design method with exhaustive search algorithm may cause prohibitive computational complexity, especially when the cardinality of 3-D constellation is large. To overcome this issue, a recursive design algorithm is proposed with a computational complexity increasing polynomially with the cardinality of 3-D constellation. Extensions of the proposed methods to the SM constellation design for massive multiple-input multiple-output transmission, generalized spatial modulation (GSM) constellation design, and the SM constellation design with transmit antenna correlation are also discussed. Simulations are done to validate those theoretical analysis, and results show that the proposed 3-D constellation design is a generalized design scheme and can be adopted in any SM/GSM systems without constraints on the number of transceiver antennas. It is also shown that the proposed approach offers better symbol-error-rate performance than other solutions.

Recursive Identification of Micropositioning Stage Based on Sandwich Model With Hysteresis

In this brief, a recursive identification method for a micropositioning stage with piezo actuators is proposed. This method utilizes a sandwich model for describing nonlinear dynamics of the stage. In this model, both power amplifier with filtering circuit and the flexure hinge with load are described by linear dynamic submodels, respectively, whereas a Duhem hysteresis submodel is employed for describing the performance of the piezo actuator. An extended recursive identification algorithm is proposed for estimating the corresponding parameters of the sandwich model, and the convergence of the proposed algorithm is analyzed. Finally, the experimental results of a real positioning stage with piezo actuators are presented and discussed.

A fast iterative recursive least squares algorithm for Wiener model identification of highly nonlinear systems

In this paper, an online identification algorithm is presented for nonlinear systems in the presence of output colored noise. The proposed method is based on extended recursive least squares (ERLS) algorithm, where the identified system is in polynomial Wiener form. To this end, an unknown intermediate signal is estimated by using an inner iterative algorithm. The iterative recursive algorithm adaptively modifies the vector of parameters of the presented Wiener model when the system parameters vary. In addition, to increase the robustness of the proposed method against variations, a robust RLS algorithm is applied to the model. Simulation results are provided to show the effectiveness of the proposed approach. Results confirm that the proposed method has fast convergence rate with robust characteristics, which increases the efficiency of the proposed model and identification approach. For instance, the FIT criterion will be achieved 92% in CSTR process where about 400 data is used.

Finite-Time Stabilization of Homogeneous Non-Lipschitz Systems

This paper focuses on the problem of finite-time stabilization of homogeneous, non-Lipschitz systems with dilations. A key contribution of this paper is the design of a virtual recursive Hölder, non-Lipschitz state feedback, which renders the non-Lipschitz systems in the special case dominated by a lower-triangular nonlinear system finite-time stable. The proof is based on a recursive design algorithm developed recently to construct the virtual Hölder continuous, finite-time stabilizer as well as a C1 positive definite and proper Lyapunov function that guarantees finite-time stability of the non-Lipschitz nonlinear systems.

Online Monitoring of Thermoacoustic Eigenmodes in Annular Combustion Systems Based on a State-Space Model

Thermoacoustic instabilities have the potential to restrict the operability window of annular combustion systems, primarily as a result of azimuthal modes. Azimuthal acoustic modes are composed of counter-rotating wave pairs, which form traveling modes, standing modes, or combinations thereof. In this work, a monitoring strategy is proposed for annular combustors, which accounts for azimuthal mode shapes. Output-only modal identification has been adapted to retrieve azimuthal eigenmodes from surrogate data, resembling acoustic measurements on an industrial gas turbine. Online monitoring of decay rate estimates can serve as a thermoacoustic stability margin, while the recovered mode shapes contain information that can be useful for control strategies. A low-order thermoacoustic model is described, requiring multiple sensors around the circumference of the combustor annulus to assess the dynamics. This model leads to a second-order state-space representation with stochastic forcing, which is used as the model structure for the identification process. Four different identification approaches are evaluated under different assumptions, concerning noise characteristics and preprocessing of the signals. Additionally, recursive algorithms for online parameter identification are tested.

Simultaneous state estimation and parameter identification in linear fractional order systems using coloured measurement noise

ABSTRACTIn the present paper, the identification and estimation problem of a single-input–single-output (SISO) fractional order state-space system will be addressed. A SISO state-space model is considered in which parameters and also state variables should be estimated. The canonical fractional order state-space system will be transformed into a regression equation by using a linear transformation and a shift operator that are appropriate for identification. The identification method provided in this paper is based on a recursive identification algorithm that has the capability of identifying the parameters of fractional order state-space system recursively. Another subject that will be addressed in this paper is a novel fractional order Kalman filter suitable for the systems with coloured measurement noise. The promising performance of the proposed methods is verified using two stable fractional order systems.

Recursive least squares algorithm for a nonlinear additive system with time delay

This paper proposes a recursive least squares algorithm for a nonlinear additive system with time delay. By the Weierstrass approximation theorem and the key term separation principle, the model can be simplified as an identification model. Based on the identification model, a recursive least squares identification algorithm is used to estimate all the unknown parameters of the time-delayed additive system. An example is provided to show the effectiveness of the proposed algorithm.

Convergence of Direct Recursive Algorithm for Identification of Preisach Hysteresis Model with Stochastic Input

We consider a recursive iterative algorithm for identification of parameters of the Preisach model, one of the most commonly used models of hysteretic input-output relationships. This online algorithm uses a simple rule for updating the values of the piecewise constant density function in the switching region at each time step. The so-called persistent excitation condition has been shown to play an important role for convergence of recursive iteration schemes when input-output data are generated by a deterministic input (such as, for example, a periodically repeated sequence of test inputs prescribed by the classical Mayergoyz identification algorithm). In this work, we assume that the input randomly fluctuates and these fluctuations can be described by a stochastic Markov process. Assuming that accurate measurements of the input and output are available, we prove the exponential convergence of the recursive identification algorithm, estimate explicitly the convergence rate, and explore which properties of the stochastic input and the algorithm affect the guaranteed convergence rate. An analogue of the persistent excitation condition suitable for analysis of stochastic Markov inputs is established. Numerical examples that test the convergence of the algorithm in the case of a time-dependent density function and in the presence of measurement noise are presented.

Extended Stochastic Gradient Identification Method for Hammerstein Model Based on Approximate Least Absolute Deviation

In order to identify the parameters of nonlinear Hammerstein model which are contaminated by colored noise and peak noise, the least absolute deviation (LAD) is selected as the objective function to solve the problem of large residual square when the identification data is disturbed by the impulse noise which obeys symmetrical alpha stable (SαS) distribution. However, LAD cannot meet the need of differentiability required by most algorithms. To improve robustness and to solve the nondifferentiable problem, an approximate least absolute deviation (ALAD) objective function is established by introducing a deterministic function to replace absolute value under certain situations. The proposed method is derived from ALAD criterion and extended stochastic gradient method. Due to the differentiability of the objective function, we can get a recursive identification algorithm which is simple and easy to calculate compared with LAD. The convergence of the proposed identification method is also proved by Lyapunov stability theory, and the simulation experiments show that the proposed method has higher accuracy and stronger robustness than the least square (LS) method in the identification of Hammerstein model with colored noise and impulse noise. The impact of impulse noise can be restrained effectively.

Convergence of the recursive identification algorithms for multivariate pseudo‐linear regressive systems

SummaryThe performance analysis of the recursive algorithms for the multivariate systems with an autoregressive moving average noise process is still open. This paper analyzes the convergence of two recursive identification algorithms, the multivariate recursive generalized extended least squares algorithm and the multivariate generalized extended stochastic gradient algorithm, for pseudo‐linear multivariate systems and proves that the parameter estimation errors consistently converge to zero under persistent excitation conditions. The simulation results show that the proposed algorithms work well. Copyright © 2015 John Wiley & Sons, Ltd.

Hybrid recursive least squares algorithm for online sequential identification using data chunks

In this paper, a hybrid recursive least squares (HRLS) algorithm for online identification using sequential chunk-by-chunk observations is proposed. By employing the optimization-based least squares (O-LS), the HRLS can be initialized with any chunk of data samples and works successively in two recursive procedures for updating the inverse matrix with minimal dimension and least rank-deficiency, and thereby contributing to fast and stable online identification. Since norms of the output weight and training errors are minimized simultaneously, the HRLS achieves high accuracy in terms of both generalization and approximation. Simulation studies and comprehensive comparisons demonstrate that the HRLS is numerically more stable and superior to other algorithms in terms of accuracy and speed.