Extended Least-squares Method Research Articles

Maximum likelihood-based recursive least-squares estimation for multivariable systems using the data filtering technique

ABSTRACTFor multivariable equation-error systems with an autoregressive moving average noise, this paper applies the decomposition technique to transform a multivariable model into several identification sub-models based on the number of the system outputs, and derives a data filtering and maximum likelihood-based recursive least-squares algorithm to reduce the computation complexity and improve the parameter estimation accuracy. A multivariable recursive generalised extended least-squares method and a filtering-based recursive extended least-squares method are presented to show the effectiveness of the proposed algorithm. The simulation results indicate that the proposed method is effective and can produce more accurate parameter estimates than the compared methods.

Two-stage ARMAX Parameter Identification Based on Bias-eliminated Least Squares Estimation and Durbin's Method

This paper proposes a two-stage identification approach for the parameter identification of autoregressive moving average with exogenous variable(ARMAX) model.First,a bias-eliminated least squares method is employed to identify the autoregressive part with exogenous variable(ARX) .Then,the Durbin s method is employed to transform the parameter identification of the moving average(MA) part into that of a long autoregressive(AR) model.The MA parameters are derived directly from the parameter relationship between the MA part and its equivalent long AR model.Finally,the noise variance can be computed by using the identified MA parameters.The performance comparison against the extended least-squares method in numerical simulations validates the effectiveness of the two-stage identification approach.

Extrapolation of historical coastal storm wave data with best-fit distribution function

Extreme or design wave heights are often extrapolated from historical storm wave data with an assigned “best-fit” probability distribution function. However, there is no detailed selection criterion on how to select a best-fit distribution from a pool of candidate distributions. This study is to develop this criterion. The 19-year wave data collected off the coast of Sydney in the Tasman Sea is used and analysed to obtain a large sample of peak storm wave heights with the peaks-of-threshold method. With the least-squares method, eight commonly-used candidate distributions, the lognormal, Weibull, FT-I, II and III from the generalised extreme value distribution, and GPD-I, II and III from the generalised Pareto distribution, are all fitted to the storm wave height data to determine the best-fit distribution. An extended least-squares method is also presented to estimate the shape parameter for the three-parameter distributions. It is found that the FT-III and GPD-III with the upper bounded end intend to underestimate extreme wave heights. The observed large storm wave heights are shown to be underestimated by the lognormal, but overestimated by the GPD-I or exponential. Both the FT-I and the Weibull are found to give an equally good fit to the storm wave data. Based on the findings of this study, the general selection criterion is then developed to be unboundedness, goodness of fit, simplicity and confidence level. According to this new criterion, the FT-I distribution of the eight candidates can be uniquely determined to be the best-fit distribution for extrapolation of the historical storm wave data. This general criterion can also be used to select a best-fit distribution for extrapolation of historical wave data collected at the other NSW coastal locations or at any other coasts.

Modelling Temperature Trends in New Zealand

If global warming is accelerating, then one might expect temperatures for most stations to be accelerating and perhaps variability to be increasing. In this study, we examine 57 New Zealand temperature time series for evidence of non-linearity and changing variability. These correspond to time series for annual minima, annual means and annual maxima for 19 stations. Estimation is by an extended least-squares method. We find a surprising diversity of behaviour of these series – presumably reflecting their different geographic factors as well as series length. We give evidence of regions where temperatures are decreasing. For series where a linear trend is significant, it is downwards in about one third of the cases. This proportion was higher in the South Island, especially for series of minima. Where a non-linear trend is significant, temperatures are decelerating in about one half of the cases. The ratio of downward to upward trends is highest among annual maxima and South Island minima and smallest in annual means. Where a linear trend in the variability is significant, it is decreasing in 13 cases and increasing in 5 cases, although possibly this is partly due to poorer quality data last century. Where a non-linear trend in the variability is significant, variability is decelerating in about two thirds of the cases. The results are used to project upper and lower return levels of minima, means and maxima for each of the series to the year 2010.

Modelling time series when mean and variability both change

An extended least-squares method is described which allows us to model the location and scale of a process parametrically without specifying any parametric form for the distribution of the errors. The degree of the associated polynomials is chosen using a step-down method on a table of p-values. A pseudo-likelihood ratio test is given. The concepts of upper and lower return levels are extended to non-stationary series. The method is applied to annual means and extremes of Auckland temperatures. Evidence is found that the mean is changing non-linearly and the variance is also changing for all three series.

Identification of Blimp Dynamics via Flight Tests

A blimp is introduced as a stable platform for remote-sensing instruments required for unmanned aerial observation and surveillance. In order to develop flight control systems for a blimp, two series of experiments were conducted to identify flight dynamics: constrained flight tests, and indoor free-flight tests. This paper addresses the blimp configuration, experimental set-up, method for identifying dynamics, and the results of identification in comparison with the analytical estimation for each experimental method. Both tests employed a full-scale blimp. The identification method for the constrained flight tests used the extended least-squares method involving the gradient algorithm, and the indoor free-flight tests, the eigen-system realization algorithm involving the autoregressive model fitting algorithm. The results suggest that analytical formulas for estimating the parameters, including added mass effects and stability derivatives, may yield values consistent with experimentally identified ones.

Identification Technology of Frequency Response of Plant in Steel Rolling Process

An identification method of the frequency responses of actual plant was investigated for steel rolling control system. It is important for achieving the highest control accuracy to identify the frequency responses of actual plant and to design and to tune the controller of the system properly. Therefore, according to various rolling data measured during really operating, identification method based on extended least-squares method which estimates the parameters of ARMAX model under condition of the specified steady state gain constraint of the controlled system was tried. And the effectiveness of this method for the feed-forward gage control system of the reversing cold mill was certified.

Bilinear Identification of Nonlinear Processes

Identification of nonlinear processes using bilinear models is presented. To avoid direct estimation of the bilinear model parameters, a dynamically equivalent input/output model structure is developed through an analysis of the observability of the bilinear system. Calculation of the Volterra kernels from the input/output model parameters is presented and the overparameterization of the input/output model form is examined by comparison with the Volterra series model form. Constraint equations calculated from this guarantees the dynamic equivalence of the input/output and state-space forms. The input/output model parameters are estimated through an extended least-squares method. An example of a fluid catalytic cracking unit (FCCU) is presented.

An approach to forecast aminoglycoside-related nephrotoxicity from routinely collected clinical data.

Routinely collected clinical data on 104 critically ill patients who had received an aminoglycoside (gentamicin or tobramycin) were evaluated using a proposed approach to forecast aminoglycoside-related nephrotoxicity. Observed steady-state peak and trough concentrations were greater than the respective predicted values when one-compartment model was assumed. This difference was particularly eminent for trough concentrations. The bias (difference between predicted and observed values) for trough concentrations was analyzed assuming tissue accumulation by an extended least-squares method to estimate population pharmacokinetics. The mean values for terminal half-life of gentamicin and tobramycin in patients who did not develop nephrotoxicity were estimated to be approximately 50 and 116 h, respectively. By using these values, the bias of trough concentration was found to be greater in patients who developed nephrotoxicity during or within 60 days after the therapy than in those who did not. Our results suggest that assessing the bias of steady-state trough concentrations of aminoglycosides can provide a useful index to forecast an aminoglycoside-induced nephrotoxicity.

Identification of Stochastic Feedback Control Systems

Estimates for unknown orders and matrix coefficients of the feedback control system described by CARMA model are obtained on the basis of the extended least-squares method by minimizing a new information criterion, without requiring stationarity and ergodicity of the input and driven noise. Conditions guaranteeing consistency of the estimates are easily satisfied for adaptive control systems with control attenuately excited. The order estimation method given in this paper can efficiently be used for a large class of non-stationary time series.

A note on confidence intervals with extended least squares parameter estimates.

It has previously been shown that the extended least squares (ELS) method for fitting pharmacokinetic models behaves better than other methods when there is possible heteroscedasticity (unequal error variance) in the data. Confidence intervals for pharmacokinetic parameters, at the target confidence level of 95%, computed in simulations with several pharmacokinetic and error variance models, using a theoretically reasonable approximation to the asymptotic covariance matrix of the ELS parameter estimator, are found to include the true parameter values considerably less than 95% of the time. Intervals with the ordinary least squares method perform better. Two adjustments to the ELS confidence intervals, taken together, result in better performance. These are: (i) apply a bias correction to the ELS estimate of variance, which results in wider confidence intervals, and (ii) use confidence intervals with a target level of 99% to obtain confidence intervals with actual level closer to 95%. Kineticists wishing to use the ELS method may wish to use these adjustments.

A recursive (on-line) identification of bilinear systems

A recursive identification of a discrete dynamical system is presented in this paper. Two methods of recursive identification, namely the recursive extended least-squares method and the recursive maximum likelihood method, are described and analysed. The techniques are illustrated numerically with simulations.

Self-tuning control application to a nuclear power plant

The aim of this paper is to investigate the application possibilities of a self-tuning control method to a pressurized-water reactor (PWR) nuclear power plant. A self-tuning control algorithm which incorporates pole assignment into the generalized minimum variance strategy with a particular form of cost function is employed. This algorithm enables closed-loop system stability characteristics to be readily specified and facilitates reference following. The control system design is based on a second-order linear model with unknown, time-varying parameters. To ensure that this low-order model describes the complex real dynamics well enough for control purposes, control parameters are updated on-line with a recursive estimation sequences of the extended least-squares method. Weighting polynomials are also adjusted on-line to keep closed-loop poles at the desired location and to satisfy the zero steady-state condition and disturbance rejection. The purpose of this control system is to hold the average coolant ...

Dedicated microprocessors for realtime identification of multivariable systems

In this paper, an algorithm is proposed for identifying multivariable systems in state-space form from noisy data, which is suitable for implementation on dedicated microprocessor systems. The proposed algorithm uses the normalized stochastic approximation criterion which reduces the computational complexity and memory requirements. It is shown that the overall performance of the proposed stochastic approximation algorithm when using a dedicated microprocessor with fixed point arithmetic is superior to the extended least-squares method in terms of memory requirements, execution speed per iteration, and the estimation results.

Rapid parameter estimation algorithms using the ELS principle

Two computationally efficient algorithms for estimating the parameters of linear discrete-time systems are proposed. The algorithms are based on the extended least squares (ELS) principle. They are essentially a correlation version of the off-line ELS method that eliminate all the redundant computations, do not require construction and operations of large matrices and bypass the explicit evaluation of residuals. Examples are given to illustrate their feasibility and performance.

Identification of a Liquid-Saturated Steam Heat Exchanger

In this paper, the identification of a simulated liquid - saturated steam heat exchanger is dealt with. Precisely, the dependence of the outlet liquid temperature upon the liquid flow-rate is described by means of an ARMAX model. To this end, the design of a suitable identification experiment is first discussed. Subsequently, a number of different order models are identified by means of the Extended Least-Squares method. The final selection is based upon the consideration of the Akaike and Rissanen order selection criteria as well as upon the analysis of the correlation function of the model prediction error.

Dedicated Microprocessors for Real-Time Identification of Multivariable Systems

In this paper, an algorithm is proposed for identifying multi-variable systems in state-space form from noisy data, which is suitable for implementation on dedicated microprocessor systems. The proposed algorithm uses the normalized stochastic approximation criterion which reduces the computational complexity and memory requirements. It is shown that the overall performance of the proposed stochastic approximation algorithm when using dedicated microprocessor is superior to the extended least-squares method in terms of memory requirements, execution speed per iteration, and the estimation results.