Output Error Algorithm Research Articles

Wiener Nonlinear System Identification Using Fractional Model

Modeling and identification of some real processes is a task that is realized with a better accuracy using fractional nonlinear models. In this paper, identification of a fractional nonlinear Wiener system is considered. This model is a case of a block-oriented structure, which consists of a linear time invariant fractional system connected to a static non linearity. An output error algorithm is developed to estimate the parameters of the system as well as the fractional order. The proposed algorithm efficiency is tested on a simulation example.

A Branch and Bound Approach to System Identification based on Fixed-rank Hankel Matrix Optimization

We consider identification of linear systems with a certain order from a set of noisy input-output observations. We utilize the fact that the system order corresponds to the rank of the Hankel matrix associated with the system impulse response. Then, the system identification problem is formulated as the minimization of the output error subject to a rank constraint on a Hankel matrix. As this problem is non-convex, we propose a branch and bound (BB) solver, which is a powerful tool for solving non-convex problems to optimality. The main ingredients of the proposed BB method are a convex relaxation problem and a local minimizer of the original non-convex problem. We illustrate the promising performance of the proposed scheme in a system identification problem. The results demonstrate the higher accuracy and stability of our method in estimating the true system compared to the standard output error (OE) algorithm.

Initialization of Identification of Fractional Model by Output-Error Technique

A bad initialization of output-error (OE) technique can lead to an inappropriate identification results. In this paper, we introduce a solution to this problem; the basic idea is to estimate the parameters and the fractional order of the noninteger system by a new approach of least-squares (LS) method based on repeated fractional integration to initialize OE technique. It will be shown that LS method offers a good initialization to OE algorithm and leads to acceptable identification results. The performance of the proposed method is shown through numerical simulation examples.

An Identification Procedure For The Tuning Of A Robust Fractional Controller

An identification procedure for the tuning of a robust fractional controller is proposed in the paper. The fractional controller is a time delay fractional PID controller, adapted to a large class of systems, and insuring robustness to static gain variations. The identification procedure, based on the Output Error algorithm, permits to define a worst case model, used to tune the fractional controller, in order to provide robustness to identification uncertainties. Numerical experiments illustrate the different steps of this tuning procedure.

An output error algorithm for piecewise affine system identification

Within Hybrid systems, piecewise affine systems are a common class to be identified from input/output data. In this paper an improved algorithm for identifying piecewise affine systems is developed. The algorithm stems from clustering-based system identification. An affine output error algorithm is used to identify final models. The performance of the new Piecewise Affine Output Error (PWA-OE) algorithm is demonstrated using experimental data from a Radio Frequency MicroElectroMechanical Systems switch. Compared to the existing state-of-the-art, the PWA-OE algorithm generates a potential 62% improvement in model coefficient accuracy. Furthermore the PWA-OE algorithm is less sensitive to two additional input parameter selections.

Results of Short-Period Helicopter System Identification Using Output-Error and Hybrid Search-Gradient Optimization Algorithm

This article focuses on the problem of parameter estimation of the uncoupled, linear, short-period aerodynamic derivatives of a “Twin Squirrel” helicopter in level flight and constant speed. A flight test campaign is described with respect to maneuver specification, flight test instrumentation, and experimental data collection used to estimate the aerodynamic derivatives. The identification problem is solved in the time domain using the output-error approach, with a combination of Genetic Algorithm (GA) and Levenberg-Marquardt optimization algorithms. The advantages of this hybrid GA and gradient-search methodology in helicopter system identification are discussed.

Initialization of output-error identification methods – Comparison between ARX and RPM models

The main disadvantage of the Output-Error (OE) identification methods is that they may converge to a secondary optimum. A good initialization converges to the global optimum. The ARX model is often selected as initialization step to OE algorithms. However, the ARX model may be too biased and may not lead to a good initialization. This paper presents an approach based on the Reinitialized Partial Moment (RPM) to obtain a good initialization for OE methods. The RPM model presents an implicit filter that replaces the necessary explicit filter required by the ARX model. The result are encouraging and they have shown that the RPM based approach has to lead to a better initialization than the conventional techniques.

Calibration of 5-hole Probe for Flow Angles from Advanced Technologies Testing Aircraft System Flight Data

This paper describes the investigations carried out to calibrate the 5-hole probe for flow angles from advanced technologies testing aircraft system flight data. The flight tests were carried out with gear up and at nominal mid-centre of gravity location for two landing flap positions, *df = IN and 14?. Dynamic manoeuvres were executed to excite the short period and Dutch roll mode of the aircraft. In addition, pull up, push down and steady sideslip manoeuvres were also carried out. The data compatibility check on the recorded flight data has been carried out using maximum likelihood output error algorithm to estimate the bias, scale factor, and time delay in the pressure measurements from the 5-hole probe mounted on a noseboom in front of aircraft nose. Through a way of kinematic consistency checking, flight-validated scale factors, biases, and time delays are determined for the differential pressure measurements for both angle of attack and angle of sideslip. Also, the dynamic pressure measurement is found to have time delays. Based on the earlier investigations, it is once again confirmed that the measurements of attitude angles, obtained from the inertial platform, clearly indicate time delays referred to the other signals like linear accelerations and angular rates which are measured with the dedicated flight instrumentation package. The identified time delays in attitude angles agreed well with the inertial platform specifications. The estimates of sensitivity coefficients and scale factors from the flight data analysis correlates reasonably well with the manufacturer Rosemount calibration curves for the tested Mach range 0.23-0.53. The flight data analysis at Mach number of about 0.59 indicate Mach dependency for the angle of attack.13;

A Methodology for Estimation of Physical Parameters

This article deals with the estimation of physical parameters. This estimation is performed using an Output Error algorithm based on nonlinear optimization. Output Error techniques permit to obtain unbiased estimation and can be applied either to linear systems or nonlinear ones. The usual quadratic criterion is modified in order to include prior physical knowledge. A deterministic interpretation of this criterion is given in the linear parameter case and in the nonlinear parameter one. Estimation is also improved using direct optimization by physical parameters, owing to a generalized formulation of sensitivity functions. A real electrical engineering example illustrates the efficiency of this methodology.

An adaptive IIR filter algorithm based on observers

The output error approach to adaptive IIR filtering is considered from a state observation perspective, and a new algorithm, termed the observer-based regressor filtering (OBRF) algorithm, is developed. The convergence requirements of the OBRF are established as a persistent excitation condition on the regressor and a strict positive reality (SPR) condition on an operator arising in the algorithm. Speed of convergence experiments show that the OBRF algorithm converges more quickly than the related output error algorithm for the hyperstable adaptive recursive filter (HARF), although the OBRF algorithm converges as quickly as typical equation error schemes. The OBRF is shown to compare favorably with equation error with respect to parameter bias in the presence of output measurement noise. Thus, OBRF is a compromise between the equation error and output error approaches. In addition, algorithm parameter selection to satisfy the SPR condition for OBRF is explored and compared with the related conditions for HARF.

Comparison of the closed-loop identification methods in terms of the bias distribution

Several schemes for plant model identification in closed-loop operation including classical direct method, two-step identification and closed-loop output error algorithms are considered. These methods are analyzed and compared in terms of the bias distribution of the estimates for the case that the noise model is estimated as well as the case that a fixed model of noise is considered (output error structure). The problems concerning the filtered direct method which is often used in the iterative identification and control scheme are mentioned. It is shown that these problems may be solved by the closed-loop output error identification method.

On the bias of the modified output error algorithm

In a recent work by Betser and Zeheb (1995), a modified adaptive output error algorithm for identification was proposed. In this paper, we prove that the solution is biased for most practical types of disturbance noise, including the white noise case. Bias can be avoided in certain cases, under the verification of a relation between the spectrum of the noise and the noise-free solution, specified in the form of a theorem.

Modified output error identification-elimination of the SPR condition

In this note, we present a modified adaptive output error algorithm for identification. We refer to both the continuous time and the discrete time cases. In the standard algorithm, stability requires that a certain transfer function should be strictly positive real (SPR); however, in the present algorithm, the SPR condition, which is difficult to satisfy, is eliminated. This is achieved by adding a fixed feedback gain. When there exists an a priori partial knowledge about the parameters of the plant, we provide a simple procedure to design that gain. An illustrative example comparing the modified algorithm to the standard one is provided. >

Adaptive lattice bilinear filters

Two fast least-squares lattice algorithms for adaptive nonlinear filters equipped with bilinear system models are presented. The lattice filter formulation transforms the nonlinear filtering problem into an equivalent multichannel linear filtering problem, thus using multichannel lattice filtering algorithms to solve the nonlinear filtering problem. The computational complexity of the algorithms is an order of magnitude smaller than that of previously available methods. The first of the two approaches is an equation error algorithm that uses the measured desired response signal directly to compute the adaptive filter outputs. This method is conceptually very simple, but results in biased system models in the presence of measurement noise. The second is an approximate least-squares output error solution; the past samples of the output of the adaptive system itself are used to produce the filter output at the current time. Results indicate that the output error algorithm is less sensitive to output measurement noise than the equation error method. >

The composite regressor algorithm for IIR adaptive systems

An adaptive IIR algorithm called the composite regressor algorithm (CRA) is developed. The algorithm is a generalization of the common equation error, a priori output error, and a posteriori output error adaptive IIR algorithms. The CRA is analyzed for convergence in a noiseless environment and for bias in a stochastic setting. It is determined that, by using a parameter called the regressor composition parameter, a tradeoff can be obtained between the automatic convergence but large bias results of the equation error algorithm and the difficult convergence condition but small bias results of the output error algorithms. In proving results for the CRA, it is shown that the a posteriori output error algorithm produces estimates with nonzero bias when the adaptive gain is small but bounded away from zero. A convergence condition for the a priori output error algorithm is derived for the first time. >

Identification/prediction algorithms for armax models with relaxed positive real conditions

AbstractExtended least squares (ELS) algorithms are proposed for ARMAX model identification with the objective of avoiding the positive real condition associated with standard equation error and output error algorithms. This is achieved by an overparametrization at the cost of additional richness requirements on excitation signals, but without introducing ill‐conditioning or infinite‐dimensional calculations as in earlier methods. Results for the case of D‐step‐ahead prediction ELS algorithms for ARMAX models are also explored in the paper. Some simulation studies are included to assess the relative performance characteristics of the proposed algorithms, and the nature of the relaxed positive real condition for different degrees of overparametrization N is investigated in detail for second‐order noise models.

Adaptive algorithms with filtered regressor and filtered error

This paper presents a unified framework for the analysis of several discrete time adaptive parameter estimation algorithms, including RML with nonvanishing stepsize, several ARMAX identifiers, the Landau-style output error algorithms, and certain others for which no stability proof has yet appeared. A general algorithmic form is defined, incorporating a linear time-varying regressor filter and a linear time-varying error filter. Local convergence of the parameters in nonideal (or noisy) environments is shown via averaging theory under suitable assumptions of persistence of excitation, small stepsize, and passivity. The excitation conditions can often be transferred to conditions on external signals, and a small stepsize is appropriate in a wide range of applications. The required passivity is demonstrated for several special cases of the general algorithm.

Tracking time-varying properties of the systemic vascular bed.

The problem of tracking changes in viscoelastic properties of the systemic arterial bed is considered and a recursive estimation procedure, belonging to the class of output-error algorithms with adjustable compensator, is developed and discussed. By means of computer simulations, suitable values are determined for the key design variable which controls the tradeoff between tracking ability and noise sensitivity of the algorithm. In this way, the algorithm allows on-line estimation of arterial compliance, peripheral resistance, and characteristic impedance on the basis of aortic pressure and flow signals. Furthermore, the results obtained from data numerically simulated, as well as measured on a mock circulatory system, demonstrate that the dominant arterial time-constant can be tracked by the algorithm using only measurements of the aortic pressure during diastole.

An output error model and algorithm for electromagnetic system identification

The identification problem for electromagnetic objects excited by transients is discussed. Several classes of models are reviewed, and an output error model is selected. An algorithm for solving the transient identification problem using this model is presented, and some of the issues connected with its use are considered. Examples of the application of this algorithm to electromagnetic data are given.

Examination of the SPR condition in output error parameter estimation

When the SPR condition is not satisfied then there exist input signals for which the considered output error algorithm is locally unstable. A condition is given which delimits the sharp stability-instability boundary in the case of slow estimation, whereas local stability properties are guaranteed by a more conservative signal-dependent average SPR condition. These conditions are also illustrated by an example.