Recursive Least-squares Approach Research Articles

Real-time state of charge and capacity estimations of vanadium redox flow battery based on unscented Kalman filter with a forgetting factor

The monitoring of the state of charge (SOC) and capacity of the vanadium redox flow battery (VRFB) is challenging due to the complex electrochemical reactions. In addition, the apparent nonlinearity and time-varying nature of the battery increase the difficulty of monitoring. Herein, we propose an unscented Kalman filtering approach with a forgetting factor, which considers the impact of the battery's historical states on the current state without remarkably increasing computational cost, to observe the battery SOC precisely. By accurately estimating the SOC, the exact capacity is acquired with the ampere-hour method, which has extreme precision requirements for the SOC. To implement the proposed method, an equivalent circuit model with a first-order branch is constructed to catch the VRFB dynamics without considering its intricate chemical behaviors. Moreover, the recursive least-squares approach is used to extract the model parameters online to improve model accuracy. Experiments were carefully conducted on a self-assembled VRFB with the constant current charge profile and the defined hybrid pulse discharge profile to validate the novel method under five charge-discharge cycles. The results denote that the proposed method enables faster estimation convergence conditions as well as realizes accurate high-fidelity monitoring of the SOC and capacity with higher stability after convergence under the same conditions than other methods.

A Recursive Least-Squares Approach with Memorizing Factor for Deriving Dynamic Equivalents of Power Systems

In this research, a two-stage identification-based approach is proposed to obtain a two-machine equivalent (TME) system of an interconnected power system for transient stability studies. To estimate the parameters of the equivalent system, a three-phase fault is applied near and/or at the bus of a local machine in the original multimachine system. The electrical parameters of the equivalent system are calculated in the first stage by equating the active and reactive powers of the local machine in both the original and the predefined equivalent systems. The mechanical parameters are estimated in the second stage by using a recursive least-squares estimation (RLSE) technique with a factor called “memorizing factor”. The approach is demonstrated on New England 10-machine 39-bus system, and its accuracy and efficiency are verified by computer simulation in MATLAB software. The results obtained from the TME system agree well with those obtained from the original multimachine system.

Online inertia estimation for power systems with high penetration of RES using recursive parameters estimation

Low and time-changing inertia values due to the high percentage of renewable energy sources (RESs) can cause stability problems in power systems due to rapid frequency instabilities. Inertia monitoring will assist operators to apply suitable actions and more proper control methods to alleviate stability issues. Therefore, this paper proposes an online method to estimate the total inertia of a network using a recursive least-squares approach. The proposed method uses network measurements with a non-recursive system identification approach to initially estimate the network hypothesis model. Then, the recursive method is used together with time changing measurements to recursively estimate model parameters and extract online inertia estimates of the network. During the estimation, the method does not need to store previous data after each sample step; therefore, the computation burden is significantly reduced. More importantly, the technique incorporates the use of available electromechanical oscillation modes in the system, which are linked with system parameters, to determine the network inertia estimates. The applicability of the proposed method has been validated by numerical simulations of the IEEE 39-bus network and the aggregated New Zealand network with its actual inertia data.

Non-stationary concept of accident prediction

This paper aims to develop a model to improve road safety based on the spatial and temporal features of accident occurrence. The spatial distribution characteristic of an accident follows a probability density function (PDF) that can be estimated with parametric functions. Estimating the PDF of accidents can help road specialists recognise accident-prone locations and improve road safety through countermeasures. In this study, the PDF of accidents is estimated using Gaussian mixture models. Gaussian models possess local and density information about accident distributions. For the prediction step, the parameters of the Gaussian models are predicted by means of a recursive least-squares approach. The major feature of this study is that the proposed model can accurately predict physical points where accidents are more likely to take place in the upcoming year. Moreover, because of the non-stationary feature of accidents, the proposed model is online, implying that it would update itself annually. The range of errors obtained from the results of cross-validation with existing data provides a very good indication of the accuracy of the proposed model.

Fuzzy Recursive Least-Squares Approach in Speech System Identification: A Transformed Domain LPC Model

In speech system identification, linear predictive coding (LPC) model is often employed due to its simple yet powerful representation of speech production model. However, the accuracy of LPC model often depends on the number and quality of past speech samples that are fed into the model; and it becomes a problem when past speech samples are not widely available or corrupted by noise. In this paper, fuzzy system is integrated into the LPC model using the recursive least-squares approach, where the fuzzy parameters are used to characterize the given speech samples. This transformed domain LPC model is called the FRLS-LPC model, in which its performance depends on the fuzzy rules and membership functions defined by the user. Based on the simulations, the FRLS-LPC model with this special property is shown to outperform the LPC model. Under the condition of limited past speech samples, simulation result shows that the synthetic speech produced by the FRLS-LPC model is better than those produced by the LPC model in terms of prediction error. Furthermore with corrupted past speech samples, the FRLS-LPC model is able to provide better reconstructed speech while the LPC model is failed to do so.

Lithium-ion battery state-of-charge estimation based on deconstructed equivalent circuit at different open-circuit voltage relaxation times

Equivalent circuit model-based state-of-charge (SOC) estimation has been widely studied for power lithium-ion batteries. An appropriate relaxation period to measure the open-circuit voltage (OCV) should be investigated to both ensure good SOC estimation accuracy and improve OCV test efficiency. Based on a battery circuit model, an SOC estimator in the combination of recursive least squares (RLS) and the extended Kalman filter is used to mitigate the error voltage between the measurement and real values of the battery OCV. To reduce the iterative computation complexity, a two-stage RLS approach is developed to identify the model parameters, the battery circuit of which is divided into two simple circuits. Then, the measurement values of the OCV at varying relaxation periods and three temperatures are sampled to establish the relationships between SOC and OCV for the developed SOC estimator. Lastly, dynamic stress test and federal test procedure drive cycles are used to validate the model-based SOC estimation method. Results show that the relationships between SOC and OCV at a short relaxation time, such as 5 min, can also drive the SOC estimator to produce a good performance.

Robust recursive impedance estimation for automotive lithium-ion batteries

Recursive algorithms, such as recursive least squares (RLS) or Kalman filters, are commonly used in battery management systems to estimate the electrical impedance of the battery cell. However, these algorithms can in some cases run into problems with bias and even divergence of the estimates. This article illuminates problems that can arise in the online estimation using recursive methods, and lists modifications to handle these issues. An algorithm is also proposed that estimates the impedance by separating the problem in two parts; one estimating the ohmic resistance with an RLS approach, and another one where the dynamic effects are estimated using an adaptive Kalman filter (AKF) that is novel in the battery field. The algorithm produces robust estimates of ohmic resistance and time constant of the battery cell in closed loop with SoC estimation, as demonstrated by both in simulations and with experimental data from a lithium-ion battery cell.

Parameter estimation of a three-axis spacecraft simulator using recursive least-squares approach with tracking differentiator and Extended Kalman Filter

Spacecraft simulators are widely used to study the dynamics, guidance, navigation, and control of a spacecraft on the ground. A spacecraft simulator can have three rotational degrees of freedom by using a spherical air-bearing to simulate a frictionless and micro-gravity space environment. The moment of inertia and center of mass are essential for control system design of ground-based three-axis spacecraft simulators. Unfortunately, they cannot be known precisely. This paper presents two approaches, i.e. a recursive least-squares (RLS) approach with tracking differentiator (TD) and Extended Kalman Filter (EKF) method, to estimate inertia parameters. The tracking differentiator (TD) filter the noise coupled with the measured signals and generate derivate of the measured signals. Combination of two TD filters in series obtains the angular accelerations that are required in RLS (TD-TD-RLS). Another method that does not need to estimate the angular accelerations is using the integrated form of dynamics equation. An extended TD (ETD) filter which can also generate the integration of the function of signals is presented for RLS (denoted as ETD-RLS). States and inertia parameters are estimated simultaneously using EKF. The observability is analyzed. All proposed methods are illustrated by simulations and experiments.

A low-computational-cost inverse heat transfer technique for convective heat transfer measurements in hypersonic flows

The measurement of the convective wall heat flux in hypersonic flows may be particularly challenging in the presence of high-temperature gradients and when using high-thermal-conductivity materials. In this case, the solution of multidimensional problems is necessary, but it considerably increases the computational cost. In this paper, a low-computational-cost inverse data reduction technique is presented. It uses a recursive least-squares approach in combination with the trust-region-reflective algorithm as optimization procedure. The computational cost is reduced by performing the discrete Fourier transform on the discrete convective heat flux function and by identifying the most relevant coefficients as objects of the optimization algorithm. In the paper, the technique is validated by means of both synthetic data, built in order to reproduce physical conditions, and experimental data, carried out in the Hypersonic Test Facility Delft at Mach 7.5 on two wind tunnel models having different thermal properties.

Algorithmic survey of parametric value function approximation.

Reinforcement learning (RL) is a machine learning answer to the optimal control problem. It consists of learning an optimal control policy through interactions with the system to be controlled, the quality of this policy being quantified by the so-called value function. A recurrent subtopic of RL concerns computing an approximation of this value function when the system is too large for an exact representation. This survey reviews state-of-the-art methods for (parametric) value function approximation by grouping them into three main categories: bootstrapping, residual, and projected fixed-point approaches. Related algorithms are derived by considering one of the associated cost functions and a specific minimization method, generally a stochastic gradient descent or a recursive least-squares approach.

Modified RLS Algorithm and Its Application to Channel Estimation for CDMA Systems

A new adaptive algorithm is proposed by introducing some modifications to the recursive least squares (RLS) algorithm. Except for the noise variance, the proposed algorithm does not require any statistics or knowledge of the desired signal, thus, it is suitable for adaptive filtering for channel estimation in code division multiple access (CDMA) systems in cases where the standard RLS approach cannot be used. A theoretical analysis demonstrates the convergence of the proposed algorithm, and simulation results for CDMA channel estimation show that the proposed algorithm outperforms existing channel estimation schemes.

Interference Robust Transmission for the Downlink of an OFDM-Based Mobile Communications System

Radio networks for future mobile communications systems, for example, 3GPP Long-Term Evolution (LTE), are likely to use an orthogonal frequency division multiplexing- (OFDM-) based air interface in the downlink with a frequency reuse factor of one to avoid frequency planning. Therefore, system capacity is limited by interference, which is particularly crucial for mobile terminals with a single receive antenna. Nevertheless, next generation mobile communications systems aim at increasing downlink throughput. In this paper, a single antenna interference cancellation (SAIC) algorithm is introduced for amplitude-shift keying (ASK) modulation schemes in combination with bit-interleaved coded OFDM. By using such a transmission strategy, high gains in comparison to a conventional OFDM transmission with quadrature amplitude modulation (QAM) can be achieved. The superior performance of the novel scheme is confirmed by an analytical bit-error probability (BEP) analysis of the SAIC receiver for a single interferer, Rayleigh fading, and uncoded transmission. For the practically more relevant multiple interferer case we present an adaptive least-mean-square (LMS) and an adaptive recursive least-squares (RLS) SAIC algorithm. We show that in particular the RLS approach enables a good tradeoff between performance and complexity and is robust even to multiple interferers.

Improved tracking of time-varying encoding properties of visual neurons by extended recursive least-squares

Traditional approaches to characterizing the transformation from stimulus to response in sensory systems assume both stationarity of the stimulus and time-invariance of the stimulus/response mapping. However, recent studies of sensory function under natural stimulus conditions have demonstrated important features of neural encoding that are in violation of these assumptions. Many sensory neurons respond to changes in the statistical distribution of the stimulus that are characteristic of the natural environment with corresponding changes in their encoding properties. In this paper, an extended recursive least-squares (ERLS) approach to adaptive estimation from stimulus/response observations is detailed. The ERLS approach improves the tracking ability of standard RLS approaches to adaptive estimation by removing a number of assumptions about the underlying system and the stimulus environment. The ERLS framework also incorporates an adaptive learning rate, so that prior knowledge of the relationship between the stimulus and the adaptive nature of the system under investigation can be used to improve tracking performance. Simulated and experimental neural responses are used to demonstrate the ability of the ERLS approach to track adaptation of encoding properties during a single stimulus/response trial. The ERLS framework lends tremendous flexibility to experimental design, facilitating the investigation of sensory function under naturalistic stimulus conditions.

Estimation of general linear model coefficients for real-time application

An algorithm using an orthogonalization procedure to estimate the coefficients of general linear models (GLM) for functional magnetic resonance imaging (fMRI) calculations is described. The idea is to convert the basis functions or explanatory variables of a GLM into orthogonal functions using the usual Gram–Schmidt orthogonalization procedure. The coefficients associated with the orthogonal functions, henceforth referred to as auxiliary coefficients, are then easily estimated by applying the orthogonality condition. The original GLM coefficients are computed from these estimates. With this formulation, the estimates can be updated when new image data become available, making the approach applicable for real-time estimation. Since the contribution of each image data is immediately incorporated into the estimated values, storing the data in memory during the estimation process becomes unnecessary, minimizing the memory requirements of the estimation process. By employing Cholesky decomposition, the algorithm is a factor of two faster than the standard recursive least-squares approach. Results of the analysis of an fMRI study using this approach showed the algorithm’s potential for real-time application.

STOCHASTIC PROGNOSTICS FOR ROLLING ELEMENT BEARINGS

The capability to accurately predict the remaining life of a rolling element bearing is prerequisite to the optimal maintenance of rotating machinery performance in terms of cost and productivity. Due to the probabilistic nature of bearing integrity and operation condition, reliable estimation of a bearing's remaining life presents a challenging aspect in the area of maintenance optimisation and catastrophic failure avoidance. Previous study has developed an adaptive prognostic methodology to estimate the rate of bearing defect growth based on a deterministic defect-propagation model. However, deterministic models are inadequate in addressing the stochastic nature of defect-propagation. In this paper, a stochastic defect-propagation model is established by instituting a lognormal random variable in a deterministic defect-propagation rate model. The resulting stochastic model is calibrated on-line by a recursive least-squares (RLS) approach without the requirement of a priori knowledge on bearing characteristics. An augmented stochastic differential equation vector is developed with the consideration of model uncertainties, parameter estimation errors, and diagnostic model inaccuracies. It involves two ordinary differential equations for the first and second moments of its random variables. Solving the two equations gives the mean path of defect propagation and its dispersion at any instance. This approach is suitable for on-line monitoring, remaining life prediction, and decision making for optimal maintenance scheduling. The methodology has been verified by numerical simulations and the experimental testing of bearing fatigue life.

Forecasting of flood and sediment by an improved time-variant diffusive model

Hydrological forecasting can provide the basis for dealing with the conflict between flood control and water use. This paper proposes a flood and sediment forecasting method for rivers by deriving an energy equation which describes the conservation of potential slope, kinetic slope, and friction slope of a river reach. The equation contains an additional term, the rate of change of stage, which has a significant effect on the propagation of flood waves, as compared with the Saint-Venant momentum equation. The energy equation has been found to provide more accurate results in the hydraulic calculation of the Han River, China, than the Saint-Venant momentum equation. Based on this energy equation, an improved diffusive model (IDM) was derived. By modelling the flood process for the Yellow River, China, the IDM was compared with the classical diffusive model (CDM) showing that the IDM gives better results. The time series form of IDM with time-variant parameters was used for real-time flood and sediment forecasting of the Yellow River. The recursive ordinary least-squares (ROLS) approach, improved by introducing an effective matrix, was used for on-line identification of parameters.

A recursive least-squares digital distance relaying algorithm

A new digital distance relaying algorithm based on the well-known theory of least-squares is developed, and the results of testing it using numerical simulation are presented. The new technique estimates the distance to the fault and the fault resistance. To minimize the computational requirements of the digital relay, a recursive least-squares approach is used. Computer simulation results of the new least-squares algorithm seem promising, indicating that it should be considered for further testing and evaluation.

Multi-Input/Multi-Output Adaptive Active Flutter Suppression for a Wing Model

The work develops and verifies experimentally a multi-input/multi-output adaptive active flutter suppression system for a built-up wing model fitted with a leading- and a trailing-edge control surface and two accelerometers. An indirect adaptive scheme, combining an identification of a discrete dynamic model followed by the design of a stabilizing control law, has been used. The identification is based on a recursive multivariable-extended least-squares approach applied to the input/output relations connecting the accelerometer signals to the control surfaces deflections, while the stabilizing controller is designed by a full-state eigenstructure assignment method. The order and structure of the control system and the tuning of its design parameters have been carried out through extensive numerical simulations aimed at the determination of an optimal compromise between system performances and computational requirements. The adaptive controller thus obtained was implemented on a wing model and tested in a wind tunnel by using two loosely coupled cooperating personal computers, one for the position servos of the control surfaces, the other for the indirect adaptive flutter suppression. The tests have demonstrated that the system is capable of achieving a significant increase of the subcritical aeroelastic damping and of the flutter speed of the wing model.

Estimating the response effect of future events based on historical analogy: A methodology and illustration on generic substitution of brand-name drug sales following patent expiration

Managerial decisions often are made with considerable uncertainty about their possible effects. In assessing such problems, we often rely in an ad hoc fashion on analogous situations in the hope that they will shed light on the possible outcomes. This paper introduces a formal methodology for transferring information or data from one situation to another. A simple recursive least-squares approach to the Bayesian data transferability problem is discussed. Focus is on the method's applicability to commonly encountered marketing problems. Empirical testing and estimation issues are discussed and illustrated in the framework of generic substitution of brand-name drug sales following patent expiration.

Recursive least—squares approach to data transferability: exposition and numerical results

Data transferability refers to the transfer of information from a set of independently estimable models to a new but structurally equivalent model for which data on some predictors are missing.Using a random-coefficient regression framework, this paper discusses a recursive least-squares approach to execute the transfer and estimator all parameters of the new model.Numerical results document the method's sensitivity to practically relevant dimension and, as such, as establish its general applicability.