Recursive Extended Least Squares Research Articles

Dynamic decoupling and compensation based on the inverted network technique and experiment research for multi-axis hydraulic road simulator

This paper presents a dynamic decoupling and compensation approach to eliminate channel interaction for a multi-axis hydraulic road simulator. Misalignment of the concentrated moving mass centroid on the entire test bench with the control point and inconsistencies in actuator dynamics leads to dynamic coupling, which deteriorates the motion performance of the system. To solve the problem, an inverted decoupling and compensation network based on an identification model is proposed. Firstly, the system is modeled using the recursive extended least square (RELS) identification method. In the feedforward compensation modeling process, the steady-state inverse is obtained using zero-magnitude error technology control (ZMETC). In addition, a finite impulse response (FIR) filter with an adaptive algorithm is employed to reduce the adverse impact of the modeling error. The proposed decoupling strategy is validated by conducting experiments using a multi-axis hydraulic road simulator. The experimental results indicate that the designed compensator can effectively decrease the cross-coupling of multi-input and multi-output (MIMO) systems. The suggested approach is also applicable to applications that necessitate the elimination of interactions between different control variables.

A Capacitance Estimation Method for DC-Link Capacitors Based on Pre-Charging Model and Noise Evaluation

DC-link capacitor is one of the significant parts of traction converters. Due to the impact of electrical stress, high temperature and humidity, its capacitance degrades faster than expected. Accurate capacitance estimation is critical to the condition monitoring of DC-link capacitors, which is also the basis of online capacitor life prediction. Currently, there is a big challenge for capacitor capacitance estimation in railway applications. The noise fluctuation of the voltage sensor may be nearly equal to that of ripple voltage, leading to the considerable errors of the existing capacitor condition monitoring methods. Therefore, a capacitance estimation method based on pre-charging model and noise evaluation is proposed in this paper. The capacitance is estimated by improved recursive extended least square (RELS). The influence of the noise can be effectively reduced and both the calculation accuracy and convergence speed can be well guaranteed through an independent noise estimation model. The proposed method has good immunity in a certain range of signal-noise ratio (SNR) or signal bias. It shows good performance in experiments.

Adaptive Multi-Parameter Estimation of Inertial Stabilization Platform with Unknown Load

In order to improve the state monitoring and adaptive control capability of inertial stabilization platforms (ISPs) with unknown loads, it is necessary to estimate the dynamic parameters comprehensively online. However, most current online estimation methods regard the system as a linear dual-inertia model which neglects the backlash and nonlinear friction torque. It reduces the accuracy of the model and leads to incomplete and low accuracy of the estimated parameters. The purpose of this research is to achieve a comprehensive and accurate online estimation of multiple parameters of ISPs and lay a foundation for state monitoring and adaptive control of ISPs. First, a dual-inertia model containing backlash and nonlinear friction torque of the motor and load is established. Then, the auto-regressive moving average (ARMA) model of the motor and load is established by the forward Euler method, which clearly expresses the online identification formula of the parameters. On this basis, the adaptive identification method based on the recursive extended least squares (RELS) algorithm is used to realize the online estimation of multiple parameters. The simulation and experimental results show that the proposed adaptive multi-parameter estimation method can realize the simultaneous online identification of the moment of inertia of the load, the damping coefficient of motor and load, the transmission stiffness, the Coulomb friction torque of motor and load, and the backlash, and the steady-state error is less than 10%. Compared with the traditional linear dual-inertia model, the similarity between the model based on the proposed adaptive parameter estimation algorithm and the actual system is increased by 65.3%.

Dynamic positioning filter design applied on the small ship

This paper investigates a filter design method for dynamic positioning control system based on the wave peak frequency tracking algorithm. The wave peak frequency varies randomly with the sea condition, ship speed, wave direction and other factors. The performance of the filter is greatly affected by the real-time recognition of the wave peak frequency. The wave disturbance model is indicated as an autoregressive moving average (ARMA) model and the recursive extended least squares (RELS) algorithm is proposed to identify the wave peak frequency with the auxiliary model idea. A filter with the wave peak frequency tracker is constructed to evaluate the effectiveness of the proposed filter. Ultimately, simulation results show that the proposed filter can effectively track the wave peak frequency and can still effectively reduce the influence of waves on the ship control system when the peak frequency changes.

A Method of Reducing Invalid Steering for AUVs Based on a Wave Peak Frequency Tracker

The motion control of autonomous underwater vehicles (AUVs) is affected by waves near the ocean surface or in shallow-water areas. Therefore, to counteract the influence of waves, we need to remove them by designing a filter. The wave peak frequency is important in wave filter design. This paper focuses on the identification of the wave peak frequency using the least-squares parameter estimation algorithm. The input–output expression of the wave disturbance model is derived by eliminating the intermediate variable. Based on the obtained identification model, an auxiliary model-based recursive extended least-squares identification algorithm is developed to estimate the model parameters. The effectiveness of the proposed method is verified with simulated tests of the heading control system of an AUV. The simulation results demonstrate that the proposed method is effective for the identification of the wave peak frequency, and an observer with a wave peak frequency tracker can significantly reduce invalid steering.

Identification of Multivariable Hammerstein CARMA System Using Special Test Signals

Abstract The multivariable Hammerstein controlled autoregressive moving average (CARMA) system contains the sum of bilinear parameter vectors in the identification model, which is difficult to be transformed into a regression form for direct identification. A two-stage identification technique is developed in this article. By using multiple sets of special test signals, this chapter achieves separable identification for the linear subsystem and the nonlinear subsystem. Then, using the property of binary signal input to nonlinear part, parameters of noise model and the linear subsystem can be calculated by recursive extended least squares (RELS) method. To implement the off-line identification, the RELS is used to identify the nonlinear subsystem parameters. Finally, simulation examples illustrate the validity of proposed approach in identifying multivariable Hammerstein CARMA system.

A constrained distributed time-series neural network MPC approach for HVAC system energy saving in a medium-large building

In this paper, heating and ventilation air conditioning system (HVAC) dataset for a medium-large size building in Romania has been used. It has been collected in one year. Linear state-space model of each air handling unit (AHU) has been estimated using two methods. Recursive extended least squares (RELS) algorithm has been used to estimate the state-space model in one year and seasonal form in the first method. In the second method, a linear time-series neural network has been used for estimating the state-space model in one year form. The constrained distributed model predictive controller has been applied to each AHU state-space model that was estimated before. Every AHU unit energy consumption has been calculated after applying DMPC controller and PI controller on estimated models using simulation results. Results have been compared with energy consumption calculated using the dataset. The mean of energy consumption reduction with 2 approaches is about 36.94%.

A Wave Peak Frequency Tracking Method Based on Two-Stage Recursive Extended Least Squares Identification Algorithm

This paper proposes the wave peak frequency tracking methods based on the least squares identification algorithm. The wave disturbance model is transformed into an autoregressive moving average (ARMA) model and a recursive extended least squares (RELS) algorithm is derived to identify the model parameters by using the auxiliary model identification idea. Furthermore, a two-stage recursive extended least squares (2S-RELS) algorithm is presented to improve the convergence speed by using the hierarchical identification principle. A ship heading control system with the wave peak frequency tracker is built to evaluate the effectiveness of the proposed algorithms. Finally, simulation results show that the proposed algorithms can estimate the wave peak frequency accurately and the 2S-RELS algorithm can improve the convergence speed effectively.

Hierarchical extended least squares estimation approaches for a multi-input multi-output stochastic system with colored noise from observation data

This paper uses the hierarchical identification principle to decompose a multi-input multi-output equation-error moving average system into two subsystems, and then proposes a decomposition-based recursive extended least squares (D-RELS) algorithm (i.e., hierarchical extended least squares algorithm) to estimate the parameter matrices of these two subsystems. Before that, a recursive extended least squares (RELS) algorithm is presented as a comparison. By analyzing the estimation results and the calculation amount, these two algorithms can estimate the system parameters effectively but the D-RELS algorithm has less computational cost than the RELS algorithm. The proposed D-RELS algorithm is extended to multi-input multi-output equation-error autoregressive moving average systems. The numerical simulation results demonstrate the effectiveness of the proposed algorithms.

Improved least‐squares identification for multiple‐output non‐linear stochastic systems

This study considers the identification problems of multiple-output non-linear equation-error moving average systems. There exist the product items of the parameters between the non-linear and linear parts. To solve this difficulty, the key term separation technique is adopted. By using the model decomposition technique and the hierarchical identification principle, a maximum likelihood-based recursive extended least-squares estimation algorithm with reduced computational complexity is presented to estimate the parameters of the non-linear part and the linear part interactively. The simulation results demonstrate the effectiveness of the proposed method.

Adaptive MIMO pole placement control for commissioning of a rotor system with active magnetic bearings

Active magnetic bearing (AMB) supported rotor systems require advanced control strategies to meet the increased performance requirements of more and more demanding applications. To meet the particular requirements for the performance under changing dynamics, an adaptive control structure is a task worth pursuing. This paper studies adaptive multi-input multi-output (MIMO) pole placement applied to the control commissioning of an AMB-supported rotor system. The control tuning approach is based on a rigid body model, and the parameter estimation is carried out with a recursive extended least squares (RELS) based algorithm for the MIMO system. The proposed approach is studied by simulations and validated with both a 2-degree-of-freedom (2-DOF) and a 4-DOF AMB system.

Self-Tuning Distributed Fusion Filter for Multi-Sensor Networked Systems with Unknown Packet Receiving Rates, Noise Variances, and Model Parameters.

In this study, we researched the problem of self-tuning (ST) distributed fusion state estimation for multi-sensor networked stochastic linear discrete-time systems with unknown packet receiving rates, noise variances (NVs), and model parameters (MPs). Packet dropouts may occur when sensor data are sent to a local processor. A Bernoulli distributed stochastic variable is adopted to depict phenomena of packet dropouts. By model transformation, the identification problem of packet receiving rates is transformed into that of unknown MPs for a new augmented system. The recursive extended least squares (RELS) algorithm is used to simultaneously identify packet receiving rates and MPs in the original system. Then, a correlation function method is used to identify unknown NVs. Further, a ST distributed fusion state filter is achieved by applying identified packet receiving rates, NVs, and MPs to the corresponding optimal estimation algorithms. It is strictly proven that ST algorithms converge to optimal algorithms under the condition that the identifiers for parameters are consistent. Two examples verify the effectiveness of the proposed algorithms.

Power transformer differential protection based on least squares algorithm with extended kernel

In order to improve the dependability and security of transformer differential protection, the energisation conditions should be effectively distinguished from internal fault conditions. In this study, a new method with a low computational burden and high robustness against measurement noises is proposed for discriminating between the transformer inrush current and internal faults. In the proposed method, sine waves are fitted to the sample points of the normalised differential currents for different phases using recursive extended least-squares (RELS) algorithm in an online manner. The extended kernel enables the algorithm to effectively estimate the dynamics of the measurement noises. Three residual signals which are defined as the differences between the normalised differential currents and the fitted sine wave signals are considered as the decision criteria. Based on the selected criteria, the energisation condition is identified in about a half-cycle of power system frequency. A large number of simulation and experimental test cases are used to demonstrate the effectiveness of the proposed method. The results show that the proposed algorithm achieves an accuracy of ∼98% and has a relatively low operating time, while the computational burden for the embedded implementation is favorably low.

Recursive Least-squares Estimation for Multivariable Systems Based on the Maximum Likelihood Principle

This paper studies the identification problem of multivariable controlled autoregressive moving average systems. For the case with a parameter matrix and an unmeasurable vector in the system identification model, we transform the model into several submodels based on the number of the outputs. A maximum likelihood-based recursive least-squares algorithm is derived to identify the parameters of each submodel. A multivariable recursive extended least-squares algorithm is provided as a comparison. The effectiveness of the proposed identification algorithm is verified by simulation examples.

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.

MIMO human handwriting model in stochastic environment

The present paper deals with a multi inputs multi outputs (MIMO) human handwriting model to characterise the pen-tip displacement on the plan from two forearm muscles activities, called electromyography signals (EMG). The proposed model takes into account perturbations and incertitude whish can affect the handwriting process (instability of the writing support, psychical state of the writer, brusque movement, etc.). In this sense, an experimental approach was presented to record the displacements of a pen-tip moving on the plane and two EMG signals during the handwriting motion. The velocity of the writing and ARMAX structure are used to characterise this biological act. Recursive extended least square (RELS) algorithm is used to estimate the parameters of the proposed handwriting model. The obtained structure shows good concordance with the experimental recorded data.

Over parameterisation and optimisation approaches for identification of nonlinear stochastic systems described by Hammerstein-Wiener models

This paper proposes two iterative procedures based on over-parameterisation and optimisation approaches for the identification of nonlinear systems which can be described by Hammerstein-Wiener stochastic models. In this case, the dynamic linear part of the considered system is described by ARMAX mathematical model. The static nonlinear block is approximated by polynomial functions. The first procedure is based on a combination of the prediction error method by using the recursive approximated maximum likelihood estimator (RAML), the singular value decomposition (SVD) approach and the fuzzy techniques in order to estimate the parameters of the considered process. As for the second procedure, it includes an appropriate representation named as generalised orthonormal basis filters (GOBF) in order to reduce the complexity of the considered system. The parametric estimation problem is formulated using the recursive extended least squares (RELS) algorithm incorporated with the singular value decomposition (SVD) and fuzzy techniques in order to segregate the coupled parameters and improve the estimation quality. The validity of the developed approaches is proved by considering a nonlinear hydraulic process simulation.

Over parameterisation and optimisation approaches for identification of nonlinear stochastic systems described by Hammerstein-Wiener models

This paper proposes two iterative procedures based on over-parameterisation and optimisation approaches for the identification of nonlinear systems which can be described by Hammerstein-Wiener stochastic models. In this case, the dynamic linear part of the considered system is described by ARMAX mathematical model. The static nonlinear block is approximated by polynomial functions. The first procedure is based on a combination of the prediction error method by using the recursive approximated maximum likelihood estimator (RAML), the singular value decomposition (SVD) approach and the fuzzy techniques in order to estimate the parameters of the considered process. As for the second procedure, it includes an appropriate representation named as generalised orthonormal basis filters (GOBF) in order to reduce the complexity of the considered system. The parametric estimation problem is formulated using the recursive extended least squares (RELS) algorithm incorporated with the singular value decomposition (SVD) and fuzzy techniques in order to segregate the coupled parameters and improve the estimation quality. The validity of the developed approaches is proved by considering a nonlinear hydraulic process simulation.

Maximum Likelihood-Based Recursive Least-Squares Algorithm for Multivariable Systems with Colored Noises Using the Decomposition Technique

This paper considers the parameter estimation problems for a class of multivariable equation-error systems with colored noises. By using the decomposition technique, a multivariable system is transformed into several subsystems to reduce the computational burden, and a maximum likelihood-based recursive least-squares identification algorithm is developed for estimating the parameters of each subsystem. As a comparison, a multivariable recursive extended least-squares algorithm is presented. The analysis indicates that the proposed algorithm has lower computational complexity than the multivariable recursive extended least-squares algorithm, and the numerical simulation results demonstrate that the proposed method is effective.

Self-Tuning Distributed Fusion Filter for Multi-Sensor Systems Subject to Unknown Model Parameters and Missing Measurement Rates

A self-tuning fusion estimation problem is addressed for multi-sensor (MS) linear discrete-time stochastic systems subject to unknown model parameters (UMPs) and missing measurement rates. The phenomena of missing measurements for different sensors are described by random variable sequences obeying Bernoulli distributions. The UMPs and missing measurement rates are identified online by the recursive extended least squares (RELS) algorithms and correlation functions, respectively. A distributed fusion identifier for UMPs is presented by using matrix-weighted fusion estimation (MWFE) algorithm in the linear unbiased minimum variance sense. Furthermore, the corresponding self-tuning state estimation algorithms are obtained by substituting the identified model parameters and missing measurement rates into the local optimal filters, cross-covariance matrices (CCMs), and distribution optimal fusion filter. Finally, the convergence of the presented algorithms is analyzed. A numerical example shows the effectiveness of the presented algorithms.