NMV optimal estimation for nonlinear discrete-time multi-channel systems

Transactions of the Institute of Measurement and Control

2014

A novel model-based algorithm for fault detection in stochastic linear and non-linear systems is proposed. The non-linear minimum variance estimation technique is used to generate a residual signal, which is then used to detect actuator and sensor faults in the system. The main advantage of the approach is the simplicity of the non-linear estimator theory and the straightforward structure of the resulting solution. Simulation examples are presented to illustrate the design procedure and the type of results obtained. The results demonstrate that both actuator and sensor faults can be detected successfully

Section: Non-linear Minimum Variance Estimationmentioning

confidence: 99%

“…The main advantage of the proposed NMV estimator is that no online linearization is required, as in the EKF, and implementation is straightforward. The cost-function to be minimized is the variance of the estimation error and a relatively simple optimization procedure and solution results (Grimble, 2007).…”

Section: Introductionmentioning

confidence: 99%

Non-linear minimum variance estimation for fault detection systems

Alkaya

Transactions of the Institute of Measurement and Control

2014

“…The estimator can be designed from the spectral factor and Diophantine equation to minimize the variance of the estimation error ( [4] and [6]) given in equation (15). The estimate ˆ( ) s t t − ℓ can be generated from a nonlinear estimator of the form:…”

Section: B the Robust Wiener Optimal Estimator Solutionmentioning

confidence: 99%

Robust wiener optimal nonlinear estimation for uncertain systems

Inzerillo

2012 20th Mediterranean Conference on Control &Amp; Automation (MED)

2012

A nonlinear operator based approach to robust estimation is introduced for discrete-time systems. It involves a signal entering a communications channel with nonlinearities, transport delay and uncertainties. The measurements are assumed to be corrupted by coloured noise which is correlated with the signal to be estimated. The signal and noise model parameters are assumed to be subject to perturbations represented by random variables with known means and covariances. The theoretical solution does not involve linearization or approximations. In the limiting case of a linear system the estimator has the form of a Wiener filter in discretetime polynomial matrix system form. I. INTRODUCTIONHE optimal filter for linear systems are well known, like the Wiener ([1]) and the Kalman filter ([2, 3]) that have proved their value in applications. These are based on minimizing a statistical criterion and are optimal in an average sense. Over the last few years a new nonlinear estimation paradigm has emerged which leads to simple filters, smoothers and predictors for classes of nonlinear stochastic systems ([4-7]).There are many techniques for nonlinear estimation and the best known is the Extended Kalman Filter (EKF). The EKF has a similar structure to the Kalman filter but has a nonlinear model within the loop. To accommodate the nonlinearity the model is linearized at each time step to estimate the transition matrix and this is used to update the estimated covariance matrix. The EKF does not include a model for channel dynamics that will be included in the following and the solution involves approximations.In the following a related frequency domain or polynomial system approach to robust nonlinear estimation problems is presented. The system, signal and noise models are assumed to include uncertain elements that can be represented by linear models with probabilistic parameter deviations. The optimal robust filter, smoother, or predictor can be obtained from the results of a frequency weighted estimation problem. The estimation problem involves inferential estimation of a signal which enters a communication channel that contains nonlinearities and S. Inzerillo is with the

“…The main advantages of the proposed estimator are that no online linearisation is required, as in the extended Kalman filter, and implementation is easy. The cost function to be minimised is the variance of the estimation error and a relatively simple optimisation procedure and solution results (Grimble, 2007).…”

Section: Introductionmentioning

confidence: 99%

Experimental application of nonlinear minimum variance estimation for fault detection systems

Alkaya

International Journal of Systems Science

2014

The purpose of this paper is to present an experimental design and application of a novel model-based fault detection technique by using a nonlinear minimum variance (NMV) estimator. The NMV estimation technique is used to generate a residual signal which is then used to detect faults in the system. The main advantage of the approach is the simplicity of the nonlinear estimator theory and the straightforward structure of the resulting solution. The proposed method is implemented and validated experimentally on DC servo system. Experimental results demonstrate that the technique can produce acceptable performance in terms of fault detection and false alarm.