Key-term Separation Principle Research Articles

Parameter estimation of nonlinear systems: dwarf mongoose optimization algorithm with key term separation principle

Parameter estimation of nonlinear systems: dwarf mongoose optimization algorithm with key term separation principle

A key-term separation based least square method for Hammerstein SOC estimation model

In this paper, a Hammerstein state of charge (SOC) estimation model for lithium-ion batteries with two inputs and single output is constructed to map the relation between battery SOC and its discharge current/voltage, and a key-term separation based least square (KT-LS) algorithm is studied to identify the model parameters so as to identify the battery SOC. The thought is, by adopting the key-term separation principle, to decompose the key-term from the linear element and to substitute the expression of the nonlinear element only into the decomposed key-term, thus to express the model output as a linear auto-regression form about parameters. Then the least square algorithm is performed to optimize parameters in the reformed auto-regression form of the Hammerstein SOC system. The advantages of the explored the KT-LS algorithm contains the least parameters required, thus the calculation burden of the KT-LS algorithm is small compared with the over-parameterized model based algorithm. In the simulation experiment part, the performance of the KT-LS algorithm under different conditions are analyzed under UDDS and LA92 conditions.; the performance comparison between the KT-LS algorithm and the key-term separation based stochastic gradient (KT-SG) algorithm is carried out; the performance of the KT-LS algorithm based Hammerstein model method is compared with that of the back propagation (BP) neural network, the Long Short Term Memory (LSTM) neural network and the Extended Kalman filter (EKF) method. The simulation results show that the KT-LS algorithm based Hammerstein SOC model can effectively estimate the SOC of lithium-ion batteries.

New application of the key term separation principle

Abstract The paper deals with a new application of the key term separation principle in identification of nonlinear dynamic systems. A multiplicative form of this operator decomposition technique is proposed and applied to the Wiener model. The resulting mathematical model is linear in both the linear and the nonlinear block parameters. Illustrative examples are included.

Identification of nonlinear block-oriented systems with backlash and saturation

Abstract A new approach to modeling and identification of discrete-time nonlinear dynamic systems with input backlash and output saturation nonlinearities is presented. The proposed three-block cascade mathematical model results from successive applications of the key-term separation principle. This provides special nonlinear model description that is linear in parameters. An iterative technique with internal variable estimation is proposed for estimation of all the model parameters based on measured input/output data and minimizing the least-squares criterion. Illustrative example of cascade system identification with backlash and saturation is included.

Fractional Hammerstein system identification based on two decomposition principles

Abstract This paper deals with fractional non-linear system identification, where the Hammerstein Controlled Auto-Regression (HCAR) model is considered. The identification process is derived for the regression form of the HCAR system based on the Over-parametrization principle and the Key-term separation principle. Levenberg-Marquardt algorithm combined with each of these principles is developed to identify the fractional HCAR system. Various simulations test the efficiency of the optimization method based on these principles.

Hierarchical Newton Iterative Parameter Estimation of a Class of Input Nonlinear Systems Based on the Key Term Separation Principle

This paper investigates the identification problem for a class of input nonlinear systems whose disturbance is in the form of the moving average model. In order to improve the computation complexity, the key term separation principle is introduced to avoid the redundant parameter estimation. Based on the decomposition technique, a hierarchical Newton iterative identification method combining the key term separation principle is proposed for enhancing the estimation accuracy and handling the computational load with the presence of the high dimensional matrices. In the identification procedure, the unknown internal items or vectors are replaced with their iterative estimates. The effectiveness of the proposed identification methods is shown via a numerical simulation example.

Modelling and identification of nonlinear cascade systems with backlash input and static output nonlinearities

ABSTRACTA new approach to the parameter identification of nonlinear dynamic systems using cascade models with nonlinear dynamic, linear dynamic and nonlinear static blocks is presented. Application of the key-term separation principle provides special expressions for the corresponding nonlinear model description that are linear in parameters. A least-squares-based iterative technique is proposed allowing estimation of all the model parameters based on measured input/output data. Illustrative examples of nonlinear cascade systems identification with input backlash and nonlinear static output characteristics are included.

Decomposition-based recursive least-squares parameter estimation algorithm for Wiener-Hammerstein systems with dead-zone nonlinearity

ABSTRACTIn this paper, a decomposition-based recursive least-squares algorithm is proposed for the parameter estimation of Wiener-Hammerstein systems with dead-zone. Based on a smooth parameterisation of the dead-zone nonlinearity, the Wiener-Hammerstein systems with dead-zone can be transformed into a particular model where the parameter vector involves the least number of parameters needed for the identification model description by using the key-term separation principle. On the basis of the particular model, the hierarchical identification principle is presented to decompose the particular model into two identification subsystems, whose parameters are estimated by using a recursive least squares and the auxiliary model method. Furthermore, the convergence analysis of the proposed algorithm ensures that the estimated parameters convergence to their true values. Compared with recursive least squares algorithm and multi-innovation least-squares, the proposed algorithm can avoid the redundant parameters estimation, and meanwhile reduce the computational burden. Numerical examples and experiment are carried out to illustrate the validity of the proposed algorithm.

Identification of Nonlinear Cascade Systems with Noninvertible Piecewise Linear Input and Backlash Output Nonlinearities

Abstract The paper deals with the parameter identification of cascade nonlinear dynamic systems with noninvertible piecewise linear input nonlinearities and backlash output nonlinearities. Application of the key term separation principle provides special expressions for the corresponding nonlinear model description that are linear in parameters. A least squares based iterative technique allows estimation of all the model parameters based on measured input/output data. Simulation studies illustrate the feasibility of proposed identification method.

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.

Hierarchical multi-innovation extended stochastic gradient algorithms for input nonlinear multivariable OEMA systems by the key-term separation principle

This paper focuses on the identification of input nonlinear multivariable systems (i.e., Hammerstein multi-input multi-output nonlinear systems) described by output-error moving average models. Based on the key-term separation principle, we separate a proper key term in the nonlinear system and transform a complex nonlinear optimization problem into a pseudo-linear optimization problem which does not involve the products of the parameters between the linear parts and the nonlinear parts. Thus, a hierarchical extended stochastic gradient (H-ESG) algorithm is given and a hierarchical multi-innovation extended stochastic gradient (H-MI-ESG) algorithm is derived for the nonlinear systems. The proposed H-MI-ESG algorithm is an extension of the H-ESG algorithms. Compared with the over-parameterization-based least-squares identification algorithm, the H-ESG and H-MI-ESG algorithms have high computational efficiency. The simulation results show the effectiveness of the proposed algorithms.

Parameter estimation for nonlinear systems by using the data filtering and the multi-innovation identification theory

For Hammerstein output-error autoregressive systems, a decomposition based multi-innovation stochastic gradient (D-MISG) identification algorithm and a data filtering based multi-innovation stochastic gradient (F-MISG) identification algorithm are derived by means of the key-term separation principle and the multi-innovation identification theory. The D-MISG algorithm uses the decomposition technique to transform a Hammerstein system into two subsystems and requires less computational cost, and the F-MISG algorithm uses a linear filter to filter the input-output data and has a higher estimation accuracy for larger innovation lengths. The simulation results show that the proposed two algorithm can give satisfactory parameter estimates.

Highly Efficient Identification Methods for Dual-Rate Hammerstein Systems

This brief concerns parameter identification for a dual-rate Hammerstein CARMA system. By combining the polynomial transformation technique and the hierarchical identification principle, this brief transforms a dual-rate nonlinear Hammerstein CARMA system into a bilinear dual-rate identification model, and presents a hierarchical least squares algorithm to estimate the parameter vectors of the bilinear dual-rate identification model. Moreover, by using the key term separation principle, this brief transforms the dual-rate nonlinear Hammerstein CARMA system into a linear dual-rate identification model, and presents a key term separation based least squares algorithm to estimate the parameter vector of the linear dual-rate identification model. The two proposed methods possess higher computational efficiency compared with the previous over-parameterization least squares method in which many redundant parameters need estimating. The simulation results show the effectiveness of the two proposed algorithms.

A novel data filtering based multi-innovation stochastic gradient algorithm for Hammerstein nonlinear systems

The identification of nonlinear systems is a hot topic in the identification fields. In this paper, a data filtering based multi-innovation stochastic gradient algorithm is derived for Hammerstein nonlinear controlled autoregressive moving average systems by adopting the key-term separation principle and the data filtering technique. The proposed algorithm provides a reference to improve the identification accuracy of the nonlinear systems with colored noise. The simulation results show that the new algorithm can more effectively estimate the parameters of the Hammerstein nonlinear systems than the multi-innovation stochastic gradient algorithm.

Iterative identification methods for input nonlinear multivariable systems using the key-term separation principle

Identification for input nonlinear multivariable systems lies in that there exist the products of the parameters of the nonlinear block and the linear block. By means of the key-term separation principle, a subsystem least squares based iterative algorithm and a subsystem gradient based iterative algorithm are proposed for input nonlinear systems described by controlled autoregressive moving average models. Finally, the proposed methods are tested using numerical examples.

Identification of nonlinear cascade systems with output hysteresis based on the key term separation principle

An approach to modeling and identification of nonlinear cascade systems with a linear dynamic system and an output hysteresis is presented. The proposed mathematical model is based on the application of the key term separation principle and a special form of Coleman–Hodgdon hysteresis model. A least-squares based iterative algorithm with internal variable estimation is used for the cascade systems parameter identification. The feasibility of proposed approach is demonstrated on illustrative examples.

Multi-innovation parameter estimation for Hammerstein MIMO output-error systems based on the key-term separation

This paper uses the key-term separation principle and develops a multi-innovation stochastic gradient algorithm for Hammerstein MIMO output error systems. The basic idea is to decompose a Hammerstein MIMO system into two subsystems and to identify the parameters of each subsystem interactively. The parameter estimation accuracy can be improved with the innovation length increasing. The simulation example verifies the effectiveness of the proposed algorithm.

Multi-innovation stochastic gradient identification for Hammerstein controlled autoregressive autoregressive systems based on the filtering technique

This paper presents two estimation algorithms for Hammerstein controlled autoregressive autoregressive systems. The key-term separation principle is used to solve the problem that the identification model contains the products of the parameters of the nonlinear part and the linear part, which causes large amount of computation. To improve the parameter estimation accuracy of the stochastic gradient algorithm, we derive a forgetting factor multi-innovation generalized stochastic gradient algorithm expanding the innovation length. To improve the convergence rate, we derive a filtering-based forgetting factor multi-innovation stochastic gradient algorithm using the filtering technique. The simulation results show that the proposed algorithms are effective.

Adaptive control of Hammerstein–Wiener nonlinear systems

The Hammerstein–Wiener model is a block-oriented model, having a linear dynamic block sandwiched by two static nonlinear blocks. This note develops an adaptive controller for a special form of Hammerstein–Wiener nonlinear systems which are parameterized by the key-term separation principle. The adaptive control law and recursive parameter estimation are updated by the use of internal variable estimations. By modeling the errors due to the estimation of internal variables, we establish convergence and stability properties. Theoretical results show that parameter estimation convergence and closed-loop system stability can be guaranteed under sufficient condition. From a qualitative analysis of the sufficient condition, we introduce an adaptive weighted factor to improve the performance of the adaptive controller. Numerical examples are given to confirm the results in this paper.

Hierarchical gradient parameter estimation algorithm for Hammerstein nonlinear systems using the key term separation principle

In this paper, we use the hierarchical identification principle to decompose a Hammerstein controlled autoregressive system into three subsystems, apply the key term separation principle to express the system output as a linear combination of the system parameters, and then derive a hierarchical gradient parameter estimation algorithm for identifying all subsystems. Finally, a multi-innovation stochastic gradient algorithm is presented to improve the estimation accuracy by making full of the identification innovation. The simulation results show that the proposed algorithm is effective.