Recursive Least-squares Estimation Research Articles

Cortical brain imaging by adaptive filtering of NIRS signals

This paper presents an online brain imaging framework for cognitive tasks conducted with functional near-infrared spectroscopy (fNIRS). The measured signal at each channel is regarded as the output from a linear system with unknown coefficients. The unknown coefficients are estimated by using the recursive least squares estimation (RLSE) method. The validity of the estimated parameters is tested using the t-statistics. Contrary to the classical approach that is offline and applies the same preprocessing scheme to all channels, the proposed RLSE method for a linear model formulation provides an independent robust adaptive process for individual channels. The experiments carried out with two fNIRS instruments (continuous-wave and frequency-domain) have verified the potential of the proposed methodology which can facilitate a prompt medical diagnostics by providing real-time brain activation maps.

Adaptive weighting input estimation for nonlinear systems

This work determines the time-varying load, called input, in a nonlinear system using a novel input estimation inverse algorithm. The algorithm employs the linearised Kalman filter (LKF) with a recursive estimator to determine shocks. The LKF generates the residual innovation sequences, and the estimator uses the residual innovation sequences to evaluate the magnitudes and, therefore, the onset time histories of the shocks. Based on this regression equation, a recursive least-squares estimator weighting by an adaptive fading factor is used to estimate on-line the shocks involving measurement noise and modelling errors. Numerical simulations of a nonlinear system, Duffing's equation, demonstrate the accuracy of the proposed method, adaptive weighting input estimation. Simulation results show that the proposed method improves the accuracy, efficiency and robustness of the conventional input estimation approach.

Recursive parameter estimation for discrete-time model of an electro-hydraulic servo system with varying forgetting factor

In general, an electro-hydraulic servo (EHS) system inherently suffers from parameter uncertainties and variation which makes the modeling and controller design complicated. To encounter those difficulties, recursive least square (RLS) is often used with advanced control strategy for position, force and pressure control of the EHS system. In this paper, a new RLS estimator with varying forgetting factor was proposed for the recursive parameter estimation process. The experimental work began with an organized procedure in developing a linear discrete-time model by emphasizing the offline identification process. Best fitting criterion, final prediction errors, minimum of loss function and correlation analysis were utilized to investigate the validity of the developed model. In recursive estimation, the proposed technique gave better estimations in terms of convergence speed and accuracy as compared to the conventional approach. Furthermore, it also showed that algorithm is more sensitive to parameter changes and improves the estimation results for each estimated parameter instead of using fixed forgetting factor. Key words: Electro-hydraulic servo system, system identification, parameter estimation, recursive least square.

A new ARIMA-based neuro-fuzzy approach and swarm intelligence for time series forecasting

Time series forecasting is an important and widely interesting topic in the research of system modeling. We propose a new computational intelligence approach to the problem of time series forecasting, using a neuro-fuzzy system (NFS) with auto-regressive integrated moving average (ARIMA) models and a novel hybrid learning method. The proposed intelligent system is denoted as the NFS–ARIMA model, which is used as an adaptive nonlinear predictor to the forecasting problem. For the NFS–ARIMA, the focus is on the design of fuzzy If-Then rules, where ARIMA models are embedded in the consequent parts of If-Then rules. For the hybrid learning method, the well-known particle swarm optimization (PSO) algorithm and the recursive least-squares estimator (RLSE) are combined together in a hybrid way so that they can update the free parameters of NFS–ARIMA efficiently. The PSO is used to update the If-part parameters of the proposed predictor, and the RLSE is used to adapt the Then-part parameters. With the hybrid PSO–RLSE learning method, the NFS–ARIMA predictor may converge in fast learning pace with admirable performance. Three examples are used to test the proposed approach for forecasting ability. The results by the proposed approach are compared to other approaches. The performance comparison shows that the proposed approach performs appreciably better than the compared approaches. Through the experimental results, the proposed approach has shown excellent prediction performance.

Adaptive unified predictive control applied to first-order-plus-dead-time processes to eliminate unknown class of deterministic disturbance

A novel adaptive unified predictive control method (adaptive-UPC) is proposed and applied to the first-order-plus-dead-time (FOPDT) process models with model uncertainties (gain, time constant and dead-time) under unknown deterministic disturbances (step, ramp and the unknown frequency sinusoid). Based on indirect self-tuning regulator, this new control structure is constructed by combining UPC controller, recursive least-squares estimation with forgetting factor (RLS with forgetting factor) and variable regression estimation (VRE). By the simulation results, this scheme is proven to be applied to such process model with model uncertainties effectively.

Function Approximation with Complex Neuro-Fuzzy System Using Complex Fuzzy Sets – A New Approach

A new neuro-fuzzy computing paradigm using complex fuzzy sets is proposed in this paper. The novel computing paradigm is applied to the problem of function approximation to test its nonlinear mapping ability. A complex fuzzy set (CFS) is an extension of traditional type-1 fuzzy set whose membership is within the unit real-valued interval. For a CFS, the membership is extended to complex-valued state within the unit disc of the complex plane. For self-adaption of the proposed complex neuro-fuzzy system (CNFS), the Particle Swarm Optimization (PSO) algorithm and Recursive Least Squares Estimator (RLSE) algorithm are used in a hybrid way to adjust the free parameters of the CNFS. With the novel PSO-RLSE hybrid learning method, the CNFS parameters can be converged efficiently and quickly. By the PSO-RLSE method for the CNFS, fast learning convergence is observed and great performance in accuracy is shown. In the experimental results, the CNFS shows much better performance than its traditional neuro-fuzzy counterpart and other compared approaches. Excellent performance by the proposed approach has been shown.

An Adaptive Feedforward Compensation for Stability Enhancement in Droop-Controlled Inverter-Based Microgrids

This paper proposes an adaptive feedforward compensation that alters the dynamic coupling between a distributed-resource unit and the host microgrid, so that the robustness of the system stability to droop coefficients and network dynamic uncertainties is enhanced. The proposed feedforward strategy preserves the steady-state effect that the conventional droop mechanism exhibits and, therefore, does not compromise the steady-state power sharing regime of the microgrid or the voltage/frequency regulation. The feedforward compensation is adaptive as it is modified periodically according to the system steady-state operating point which, in turn, is estimated through an online recursive least-square estimation technique. This paper presents a discrete-time mathematical model and analytical framework for the proposed feedforward compensation. The effectiveness of the proposed control is demonstrated through time-domain simulation studies, in the PSCAD/EMTDC software environment, conducted on a detailed switched model of a sample two-unit microgrid.

Message-Efficient Location Prediction for Mobile Objects in Wireless Sensor Networks Using a Maximum Likelihood Technique

In the tracking system, a better prediction model can significantly reduce power consumption in a wireless sensor network because fewer redundant sensors will be activated to keep monitoring the object. The Gauss-Markov mobility model is one of the best mobility models to describe object trajectory because it can capture the correlation of object velocity in time. Traditionally, the Gauss-Markov parameters are estimated using an autocorrelation technique or a recursive least-squares estimation technique; either of these techniques, however, requires a large amount of historical movement information of the mobile object, which is not suitable for tracking objects in a wireless sensor network because they demand a considerable amount of message communication overhead between wireless sensors which are usually battery powered. In this paper, we develop a Gauss-Markov parameter estimator for wireless sensor networks (GMPE_MLH) using a maximum likelihood technique. The GMPE_MLH model estimates the Gauss-Markov parameters with few requirements in terms of message communication overhead. Simulations demonstrate that the GMPE_MLH model generates negligible differences between the actual and estimated values of the Gauss-Markov parameters and provides comparable prediction of the mobile object's location to the Gauss-Markov parameter estimators using an autocorrelation technique or a recursive least-squares estimation.

Adaptive fuzzy approach to function approximation with PSO and RLSE

A new adaptive fuzzy approach to function approximation is proposed in the paper. A Takagi–Sugeno (T–S) type fuzzy system is used as the function approximator in the study. The proposed approach uses a hybrid learning method to train the T–S fuzzy system to achieve high accuracy in function approximation. The hybrid learning method combines both the particle swarm optimization (PSO) and the recursive least squares estimator (RLSE) to update the parameters of the fuzzy approximator. The PSO is used to update the premise part of the fuzzy system while the consequent part is updated by the RLSE. The PSO–RLSE learning method is very efficient in learning convergence. The proposed approach is compared to other methods. Three benchmark functions are used for the performance comparison. The proposed approach shows superior performance to compared approaches, in terms of approximation accuracy and learning convergence.

A Model-Based Methodology for Real-Time Estimation of Diesel Engine Cylinder Pressure

Cylinder pressure is one of the most important parameters characterizing the combustion process in an internal combustion engine. The recent developments in engine control technologies suggest the use of cylinder pressure as a feedback signal for closed-loop combustion control. However, the sensors measuring in-cylinder pressure are typically subject to noise and offset issues, requiring signal processing methods to be applied to obtain a sufficiently accurate pressure trace. The signal conditioning implies a considerable computational burden, which ultimately limits the use of cylinder pressure sensing to laboratory testing, where the signal can be processed off-line. In order to enable closed-loop combustion control through cylinder pressure feedback, a real-time algorithm that extracts the pressure signal from the in-cylinder sensor is proposed in this study. The algorithm is based on a crank-angle based engine combustion of that predicts the in-cylinder pressure from the definition of a burn rate function. The model is then adapted to model-based estimation by applying an extended Kalman filter in conjunction with a recursive least-squares estimation scheme. The estimator is tested on a high-fidelity diesel engine simulator as well as on experimental data obtained at various operating conditions. The results obtained show the effectiveness of the estimator in reconstructing the cylinder pressure on a crank-angle basis and in rejecting measurement noise and modeling errors. Furthermore, a comparative study with a conventional signal processing method shows the advantage of using the derived estimator, especially in the presence of high signal noise (as frequently happens with low-cost sensors).

Intelligent fuzzy weighted input estimation method for the forces generated by an operating rotating machine

This paper presents a novel inverse method which efficiently and robustly estimates the vibration forces of a rotating machine mounted upon isolators under the operating condition. This new input estimation method includes the Kalman filter (KF) and the recursive least square estimator (RLSE), weighted by adopting a fuzzy weighting factor based on the fuzzy logic inference system. The excellent performance of this inverse method is demonstrated by solving the vibration problem and comparing it with constant weighting factors. The results reveal that this method has better feasibility and effectiveness in estimating vibratory forces.

Complex fuzzy model with PSO-RLSE hybrid learning approach to function approximation

A new neuro-fuzzy computing paradigm using complex fuzzy sets to the problem of function approximation is proposed in this paper. The concept of complex fuzzy sets is an extension of traditional fuzzy set whose membership degrees are within a unit disc in the complex plane. The proposed complex system has excellent input-output mapping ability. To update the free parameters of the proposed complex neuro-fuzzy system (CNFS), a novel hybrid learning method is devised, combining both the well-known particle swarm optimisation (PSO) algorithm and the recursive least squares estimator (RLSE) algorithm. By the PSO-RLSE hybrid learning method, fast learning convergence is observed and better performance in accuracy is shown. To test the proposed approach, two benchmark functions are used. The experimental results by the proposed approach are compared to its neuro-fuzzy counterpart and to other approaches in literature. According to the experiment results, excellent performance by the proposed approach has been exposed.

Recursive least-squares estimation in case of interval observation data

In the engineering sciences, observation uncertainty often consists of two main types: random variability due to uncontrollable external effects and imprecision due to remaining systematic errors in the data. Interval mathematics is well suited to treat this second type of uncertainty if set-theoretical overestimation is avoided. Overestimation means that the true range of parameter values is only quantified by rough, meaningless outer bounds. If recursively formulated estimation algorithms are used, overestimation becomes a key problem. This occurs in state-space estimation which is relevant in real-time applications and which is essentially based on recursions. Hence, overestimation has to be analysed thoroughly to minimise its impact. In this study, observation imprecision is referred to physically meaningful influence parameters. This allows to reformulate the recursion algorithm yielding an increased efficiency and to rigorously avoid overestimation. In order to illustrate and discuss the theoretical results, a damped harmonic oscillation and the monitoring of a lock are presented as examples.

Adaptive Robust Generic Model Control of High‐Purity Internal Thermally Coupled Distillation Column

AbstractThe internal thermally coupled distillation column (ITCDIC) is a frontier in energy‐saving distillation research. The process inside a high‐purity ITCDIC is of great nonlinear dynamics, which trouble the conventional control schemes. A multivariable adaptive robust generic model control (ARGMC) is presented to solve the difficulties, where an ARX model is derived and a recursive least squares estimation (RLSE) method is introduced. The benzene/toluene system is studied as an illustrative example. The results of ARGMC are compared with the robust generic model control (RGMC) and traditional PID control in detail. The performances in both servo control and regulatory control confirm the accuracy and validity of ARGMC for the high‐purity ITCDIC process.

Fast inverse prediction of phase change banks in high temperature furnaces with a Kalman filter coupled with a recursive least-square estimator

An inverse heat transfer procedure for predicting the time-varying thickness of phase-change banks on the inside surface of the walls of high temperature furnaces is presented. The main feature of the inverse method is its unique capability of making fast predictions so that it can be easily integrated to existing real-time control systems of industrial facilities. The method rests on fast computing state-space models (direct model) that are designed to mimic the response of a full finite-difference model of the phase change problem. A Kalman filter coupled with a recursive least-square estimator (inverse method) is employed to estimate the time-varying phase front position from the data collected by a temperature and/or heat flux sensor located in the furnace wall. The inverse heat transfer procedure is thoroughly tested for typical phase change conditions that prevail inside industrial facilities. The effect of the sensor type (temperature sensor or heat flux sensor), of its location and of the measurement noise on the accuracy and stability of the predicted bank thickness is investigated. It is shown that the proposed inverse heat transfer procedure becomes increasingly reliable and accurate for predicting the bank thickness as it shrinks. This feature is of the utmost interest for preventing the sudden and accidental loss of the protective banks of industrial furnaces filled with molten material. Recommendations are also made concerning the type and location of sensors.

Adaptive Feedforward Control for Gust Load Alleviation

In this paper, an adaptive feedforward control framework is proposed for the suppression of aircraft structural vibrations induced by gust perturbations to increase the resilience of the !ight control law in the presence of the aeroelastic/aeroservoelastic interactions. Currently, aircraft with nonadaptive control laws usually include roll-off or notch lters to avoid aeroelastic/aeroservoelastic interactions. However, if changes in the aircraft conguration aresignicant,the frequencies of the!exible modesof the aircraft may beshifted, andthe notchlterscould become totally ineffective. With the proposed approach, the !exible modes can be consistently estimated in real time via a proven system-identication algorithm. The identied !exible modes information is used in the proposed adaptive feedforwardcontrolalgorithmtoadjusttheparametrizationofthebasisfunctionsinafeedforwardcontroller.Along with the recursive least-squares estimate, the feedforward controller is adjusted, and the structural vibration of the aircraft induced by the gust perturbation can be largely suppressed. An F/A-18 active aeroelastic wing aeroelastic model with gust perturbation based on the linear aeroelastic solver formulation is developed as a test bed to demonstrate the proposed adaptive feedforward control algorithm.

Adaptive Control of Pressure Tracking for Polishing Process

In this paper, an adaptive controller is developed for the pressure tracking of the pressurized toolhead in order to maintain the constant contact stress for the polishing process. This is a new polishing control method, which combines the adaptive control theory and the constant stress theory of the contact model. By using an active pneumatic compliant toolhead, a recursive least-squares estimator is developed to estimate the pneumatic model, and then a minimum-degree pole-placement method is applied to design a self-tuning controller. The simulation and experiment results of the proposed controller are presented and discussed. The main advantage of the constant contact stress control is high figuring accuracy.

Intelligent fuzzy weighted input estimation method for the input force on the plate structure

The innovative intelligent fuzzy weighted input estimation method which efficiently and robustly estimates the unknown time-varying input force in on-line is presented in this paper. The algorithm includes the Kalman Filter (KF) and the recursive least square estimator (RLSE), which is weighted by the fuzzy weighting factor proposed based on the fuzzy logic inference system. To directly synthesize the Kalman filter with the estimator, this work presents an efficient robust forgetting zone, which is capable of providing a reasonable compromise between the tracking capability and the flexibility against noises. The capability of this inverse method are demonstrated in the input force estimation cases of the plate structure system. The proposed algorithm is further compared by alternating between the constant and adaptive weighting factors. The results show that this method has the properties of faster convergence in the initial response, better target tracking capability, and more effective noise and measurement bias reduction.

Online estimation and application of power grid impedance matrices based on synchronised phasor measurements

Grid impedance matrices estimation is important in monitoring and protection of wide-area power systems. In this study, a recursive least-squares estimation algorithm with a forgetting factor is presented to identify impedance parameters of power grids. This approach is based on synchronised phasor measurements and makes it possible to track changing parameters. The algorithm is tested on two power systems using MATPOWER-generated data, and case studies are conducted for estimation of grid impedances followed by voltage stability margin analysis and fault detection. The results show that the proposed method is effective for online estimation of grid impedances, fault detection and voltage stability monitoring.

Adaptive weighting input estimation of a nonlinear system

An adaptive and robust input estimation inverse methodology for determining the time-varying unknown force, named as the input, on a nonlinear system is presented. The algorithm employs the extended Kalman filter to propose a regression model between the residual innovation and the forces. Based on this regression equation, a recursive least-squares estimator weighted by an adaptive fading factor is used to estimate the force involving measurement noise and modelling errors on-line. The capabilities of the proposed algorithm are demonstrated by numerical experiments to estimate the exciting forces acting on a nonlinear system, air-damped isolator model. Results show that the proposed method, adaptive weighting input estimation, improves the efficiency and robustness of the conventional input estimation approach.