Augmented UD Identification Research Articles

Simultaneous Identification of Bidirectional Path Models Based on Process Data

In multivariate systems, the causality relationships between any two different data variables and the corresponding path models are often unknown. In this paper, the identification of bidirectional path models of a bivariate system is investigated by extending the augmented UD identification (AUDI) algorithm proposed by Niu (1992) which can simultaneously identify the order and parameters for open-loop systems with unclear physical meanings of the even columns in the data matrix. To extract more information than the AUDI algorithm for identification of bidirectional path models, we develop a novel approach based on construction of the interleave data vector and UD factorization of the data matrix. The odd and even columns of the resulting data matrix correspond to the parameters of the forward and backward path models, respectively. Moreover, the information contained in the data matrix can be evaluated to determine the causality between the two data variables. The ARMAX process with white noise is first considered. The results are then extended to the case with colored noise. Simulation results are presented to show the effectiveness of our proposed methods.

Application of augmented UD identification with selective forgetting in an adaptive control loop

Robustness of parameter estimator plays a vital role in adaptive controllers. A modified identification algorithm is proposed based on the augmented UD identification (AUDI) primary version. Augmented UD identification with selective forgetting (AUDSF) method is derived as a robust derivation of AUDI to be integrated with input-output data filtering, relative dead zone, and data normalisation features. AUDSF is incorporated by generalised predictive controller (GPC) strategy to produce an applicable adaptive control method. The comparative performances of the developed approach have been explored on two-mass spring challenging benchmark problem, which demonstrates its excellent behaviour under conducted parameter and disturbance uncertainty scenarios.

An extended AUDI algorithm for simultaneous identification of forward and backward paths in closed-loop systems

In closed-loop system identification, most of the existing methods only focus on the forward path, yet few on simultaneous identification of the forward and backward paths. Meanwhile, an augmented UD identification (AUDI) algorithm has been proved effective in open-loop system identification, but it only extracts the forward path information, while not including the backward path information provided in an augmented information matrix, which is helpful for the closed-loop system identification. In this paper, an extended AUDI (EAUDI) is proposed to simultaneously identify the model orders and parameters of both forward and backward paths of a closed-loop system. The conditions of identifiability and uniform convergence for closed-loop systems using the EAUDI algorithm are also given. The effectiveness of this algorithm is demonstrated by a numerical example.

Experimental evaluation of augmented UD identification based vibration control of smart structures

Experimental evaluation of augmented UD identification based vibration control of smart structures

Multiple model least-squares using a Lagrangemultiplier approach

Multiple model identification typically uses Levinson-type algorithms. However, the recent augmented UD identification (AUDI) algorithm has more accuracy and application potential. A derivation via Lagrange multipliers gives further insight into the AUDI approach.

ARMAX Augmented UD Identification Algorithm (AUDIX)

An ARMAX augmented UD identification (AUDIX) algorithm for systems identification is developed to identify an ARMAX model by rearranging the regressor and parameter vectors and augmenting the covariance matrix of Bierman's UD factorization algorithm. The structure of the AUDIX is particularly easy to interpret and it is a direct extension of the augmented UD identification (AUDI) which is a direct extension to the Recursive Least Squares (RLS) algorithm. The proposed algorithm permits simultaneous identification of model parameters, disturbed by a noise model, plus loss functions for all orders from 1 to n I at each step with approximately the same calculation effort as nth order RLS, in addition it has a fast convergence rate than the AUDI. Simply, this AUDIX algorithm is a least-squares estimator, with the same numerical properties as those of Bierman's UD factorization algorithm. In addition, its structure and implementation are more straightforward and easier to analyze than the UD algorithm. Therefore, the AUDIX provides a convenient and efficient basis to be used on-line in Self-Tuning or adaptive control algorithms. This is because in real applications no guarantee that it will be free from disturbances and measurement noises in addition to stochastic environments. Thus, the objective is to estimate the parameters of the model which best fit a set of observed or measured data. This model is time-varying and is used to determine the parameters of the controller to cope with the changing process characteristics. This algorithm is utilized with the self tuning control of an aeroengine and proved robustness to numerical singularities in addition to fast and good tracking. The paper contains some of the results with a general example showing the good convergence and tracking for this algorithm.

Recursive information forgetting with augmented UD identification

Fundamental analysis of information forgetting schemes in recursive identification shows that they can be classified into two basic approaches: relative and absolute forgetting. The augmented UD identification (AUDI) algorithm developed by the authors reveals that all the information pertinent to identification and information forgetting is contained in a single matrix called the augmented information matrix (AIM). The tracking ability of the recursive algorithms is determined by the relative weight that is put on to the new information contained in the regressor, compared with the information already contained in the AIM. This relative weight can be easily controlled by the simple diagonal loss function matrix produced by the AUDI method. This simplifies the interpretation of both new and existing information forgetting approaches and also provides helpful guidelines for design.

Simultaneous estimation of parameters for different orders of discrete orthonormal function models

The augmented UD identification (AUDI) method is used to simultaneously estimate parameters of all 1 to Nth-order discrete orthonormal function models in one computational step. This method is tested on different types of orthonormal functions such as the Laguerre, Kautz, FIR, and Markov-Laguerre models.

Simultaneous estimation of process parameters, noise variance, and signal-to-noise ratio

An efficient and convenient method is developed for the online estimation of the noise variance and signal-to-noise ratio (SNR) of real processes. The method can be incorporated into most parameter estimation algorithms but is particularly appropriate for the augmented UD identification (AUDI) algorithm. The on-line estimates of the variance, SNR, and parameters can be used directly in applications such as filtering and adaptive control. >

Simultaneous structure identification and parameter estimation of multivariable systems

Abstract A recursive identification algorithm for multivariable systems is developed by extending the SISO augmented UD identification (AUDI) algorithm developed by Niu, Fisher and Xiao in 1992. This least-squares type algorithm has a simple, compact structure and provides simultaneous identification of model structure and parameters, with excellent numerical properties. A multivariable input/output difference equation model is used as the model representation for identification, and it is shown how the corresponding (unique) canonical state-space representation can also be generated by a straightforward transformation. The algorithm is easier to interpret and more straightforward to implement than the corresponding RLS approaches.

An augmented UD identification algorithm

An augmented UD identification (AUDI) algorithm for system identification is developed by rearranging the data vectors and augmenting the covariance matrix of Bierman's UD factorization algorithm. The structure of the augmented information (covariance) matrix is particularly easy to interpret and it is shown that the AUDI algorithm is a direct extension of the familiar recursive least squares (RLS) algorithm. The proposed algorithm permits simultaneous identification of the model parameters plus loss functions for all orders from 1 to n at each time step with approximately the same calculation effort as «th order RLS. This provides a basis for simultaneous model order and parameter identification so that problems due to over- and under-estimation of model can be avoided. Based on its least-squares properties, numerical robustness, theoretical basis and the fact that it simultaneously estimates multiple models, the proposed AUDI algorithm is recommended for use in place of RLS and Bierman's UD factorizatio...