Forgetting Factor Method Research Articles

A novel variable step size least mean square method for adaptive micro-vibration control

The variable step size least mean square algorithm has been suggested since a number of years as a potential solution for improving the performance of least mean square algorithm. In this article, the variable step size least mean square algorithm is classified by the techniques which are used to update step size. Unfortunately, for variable step size least mean square algorithms with forgetting factor, a constant forgetting factor may slow down its convergence speed. For this reason, a variable forgetting factor method for variable step size least mean square is proposed in this article. First, the convergence analysis of a new variable step size least mean square algorithm with the variable forgetting factor is provided. Then, simulations expose the characteristics of this variable forgetting factor method. Last, a micro-vibration control experimental system is established. Four typical variable step size least mean square algorithms and their variable forgetting factor modified version are verified through experiments. The results show that the proposed variable forgetting factor method can effectively improve convergence speed while maintaining the steady-state performance of the variable step size least mean square algorithm with the constant forgetting factor.

A Method for Parameter Identification of Combined Integrating Systems

This manuscript presents a novel structure of combined integration in the process industry and proposes an efficient method for identifying its parameters. Combined integrating processes are delay-time processes that widely exist in the industry. Conventional identification methods have a low-identification accuracy, a large vibration amplitude of the identification curve, and a poor effect for this kind of process. In this paper, a new variable forgetting factor recursive least squares method was adopted to ameliorate this problem. The method could quickly track the mutation of the ideal parameters of the process and accurately identify which of the parameters has high precision, small oscillation, and a smooth curve. The simulation results indicate that the proposed method is a significant improvement compared to the ordinary recursive least squares method and the recursive least squares with a fixed forgetting factor method, and a concise program can be verified. The experimental simulation based on the actual cut tobacco rebaking industrial process shows that the proposed method has improved identification precision and the best following effect.

Parameter Identification for Lithium Ion Supercapacitor Based on a Modified RLS Method

As a kind of renewable energy source, lithium ion supercapacitors have bright prospects in national grids, new energy technologies and tram applications. It has the good features of high energy/power density, extremely low resistance, no demand for maintenance and long cycle life. In this paper, we build up the 2ndorder RC equivalent circuit model, which is based on the Thevenin equivalent circuit model. In order to improve the accuracy and stability, and achieve accurate identification of model parameters, such as OCV, R0, Rp1, Rp2, a variable forgetting factor method is introduced into the traditional fixed forgetting factor recursive least squares method. This provides a basic method and reference for the subsequent state estimation and life prediction of lithium ion supercapacitors. The accuracy of the model parameter identification method is verified by the experimental result.

Model-free adaptive control method with variable forgetting factor for unmanned surface vehicle control

We present a new type of model-free adaptive control (MFAC) method based on an adaptive forgetting factor for unmanned surface vehicle (USV) heading control under uncertain influence. Firstly, we analyze the compact form dynamic linearization based MFAC (CFDL-MFAC) method and its main problems with regard to USV heading control. Secondly, in order to address the problems of overshoot, oscillation, and slow convergence of the heading control with the MFAC method and considering the dynamics of the USV heading control subsystem, we introduce an adaptive forgetting factor into the CFDL-MFAC to arrive at the CFDL-MFAC with variable forgetting factor (CFDL-MFAC-VFF) method. Our simulation studies show that the CFDL-MFAC-VFF method yields low overshoot and low oscillations and is insensitive to changes in the system parameters and output error. Finally, our field experiments with the small USV “Dolphin-I” demonstrate the effectiveness and engineering practicability of our proposed method.

A Novel Variable Forgetting Factor Recursive Least Square Algorithm to Improve the Anti-Interference Ability of Battery Model Parameters Identification

Recursive least square (RLS) algorithms are considered as a kind of accurate parameter identification method for lithium-ion batteries. However, traditional RLS algorithms usually employ a fixed forgetting factor, which does not have adequate robustness when the algorithm has interfered. In order to solve this problem, a novel variable forgetting factor method is put forward in this paper. Comparing with traditional variable forgetting factor methods, it has higher stability and sensitivity by using some mathematic improvements. The improvements in the robustness of recursive least square with a variable forgetting factor (VFF-RLS) algorithm is verified in this paper. A Thevenin model which is frequently-used in battery management system is employed in the verification. A data loss battery working condition is designed to simulate the interference to the algorithm. A simulation platform is established in MATLAB/Simulink software, and the data used in the verification is obtained by battery experiments. The analysis indicated that the novel VFF-RLS algorithm has better robustness and convergence ability, and has an acceptable identification accuracy.

Robust adaptive online sequential extreme learning machine for predicting nonstationary data streams with outliers

Data streams online modeling and prediction is an important research direction in the field of data mining. In practical applications, data streams are often of nonstationary nature and containing outliers, hence an online learning algorithm with dynamic tracking capability as well as anti-outlier capability is urgently needed. With this in mind, this paper proposes a novel robust adaptive online sequential extreme learning machine (RA-OSELM) algorithm for the online modeling and prediction of nonstationary data streams with outliers. The RA-OSELM is developed from the famous online sequential extreme learning machine algorithm, but it uses a more robust M-estimation loss function to replace the conventional least square loss function so as to suppress the incorrect online update of the learning algorithm with respect to outliers, and hence enhances its robustness in the presence of outliers. Moreover, the RA-OSELM adopts a variable forgetting factor method to automatically track the dynamic changes of the nonstationary data streams and timely eliminate the negative impacts of the outdated data, so it tends to produce satisfying tracking results in nonstationary environments. The performances of RA-OSELM are evaluated and compared with other representative algorithms with synthetic and real data sets, and the experimental results indicate that the proposed algorithm has better adaptive tracking capability with stronger robustness than its counterparts for predicting nonstationary data streams with outliers.

An adaptive ensemble of on-line Extreme Learning Machines with variable forgetting factor for dynamic system prediction

A demand for predictive models for on-line estimation of variables is increasing in industry. As industrial processes are time-varying, on-line learning algorithms should be adaptive to capture process changes. On-line ensemble methods have been shown to provide better generalization performance than single models in changing environments. However, most on-line ensembles do not include and exclude models during on-line operation. As a result, the ensembles have limited adaptation capability. Moreover, a higher performance can be obtained by combining a selected set of most relevant models of the ensemble for the current situation, rather than combining all the models. This paper proposes a new on-line learning ensemble of regressor models using an ordered aggregation (OA) technique which is able to provide on-line predictions of variables in changing environments. OA dynamically selects an optimal size and composition of a subset of models based on the minimization of the ensemble error on the newest sample. The proposed strategy overcomes the problem of defining the optimal ensemble size, and in most cases it obtains better performance than aggregating all the models. Models are added or removed for assuring adaptation of the ensemble in changing environments. Furthermore, this paper proposes and integrates a new on-line Extreme Learning Machine (ELM) neural network model with variable forgetting factor (FF) using the directional FF method which shows superior performance in industrial applications when compared to the well-known On-line Sequential ELM (OS-ELM) algorithm. Experiments are reported to demonstrate the performance and effectiveness of the proposed methods.

Identification of maximum road friction coefficient and optimal slip ratio based on road type recognition

The identification of maximum road friction coefficient and optimal slip ratio is crucial to vehicle dynamics and control. However, it is always not easy to identify the maximum road friction coefficient with high robustness and good adaptability to various vehicle operating conditions. The existing investigations on robust identification of maximum road friction coefficient are unsatisfactory. In this paper, an identification approach based on road type recognition is proposed for the robust identification of maximum road friction coefficient and optimal slip ratio. The instantaneous road friction coefficient is estimated through the recursive least square with a forgetting factor method based on the single wheel model, and the estimated road friction coefficient and slip ratio are grouped in a set of samples in a small time interval before the current time, which are updated with time progressing. The current road type is recognized by comparing the samples of the estimated road friction coefficient with the standard road friction coefficient of each typical road, and the minimum statistical error is used as the recognition principle to improve identification robustness. Once the road type is recognized, the maximum road friction coefficient and optimal slip ratio are determined. The numerical simulation tests are conducted on two typical road friction conditions(single-friction and joint-friction) by using CarSim software. The test results show that there is little identification error between the identified maximum road friction coefficient and the pre-set value in CarSim. The proposed identification method has good robustness performance to external disturbances and good adaptability to various vehicle operating conditions and road variations, and the identification results can be used for the adjustment of vehicle active safety control strategies.

Adaptive optimal control model for building cooling and heating sources

An adaptive optimal control model for building cooling and heating sources is presented with the aim of achieving global optimization and satisfying the requirements of time and accuracy in HVAC system control. The adaptive optimal control model includes the optimal control model, parameter identification and optimization algorithm. First, the penalty function is constructed to transform constrained optimization problem into unconstrained optimization problem, and then, the fuzzy self-tuning forgetting factor method is developed for parameter identification. In the end, the genetic algorithm (GA) is used to find the optimum values for the discrete and continuous variables. Optimization is applied for the building cooling source system in a publishing house located in Changsha, China. The optimization is expected to reduce the energy consumption of the cooling source system by 7%.

A New Approach of Kernel Bandwidth Applications for Time-series Using the Example of the Prediction of the Euro's Exchange Rate

In recent years the application of kernel smoothing methods in nonparametric regression framework to financial time-series analysis has become widespread. Kernel smoothing methods have not been applied, however, to a wide range of problems arising in time-series simulations and forecasting. Forgetting factors can be both fixed and variable. Gijbels et al (1999) propose an understanding of fixed forgetting factors via kernel smoothing. However the variable forgetting approach is not mentioned. This paper describes the variable forgetting factor and the fixed forgetting factor, and establishes the linkage for the first time between the variable forgetting factor approach and kernel smoothing. The forgetting factor method uses a sample of data and estimates the value of the forgetting factor from the sample. This method fits better than a parametric approach, which uses some assumed parameters. Since the forgetting factor method is equivalent to a kernel estimation - which is a non-parametric method - it is likely to give more accurate estimates and better forecasting performance in financial time-series than a parametric one. The major area of interest in this application is whether kernel estimation, using Cho's approach [see Cho et al (1991) and Brailsford et al (2002)] for kernel bandwidth selection, can improve the Euro's forecasting performance within the framework of subset AR modelling. The forecasting performance is compared with the performance of AR modelling without the use of the forgetting factor. If improved forecasting performance is achieved, this can increase the potential use of kernel smoothing methods in time-series forecasting. The findings show that the kernel bandwidth so determined can improve the forecasting performance.

Adaptive RBFNN versus conventional self-tuning: comparison of two parametric model approaches for non-linear control

In this work a practical study evaluates two parametric modelling approaches — linear and non-linear (neural) — for automatic adaptive control. The neural adaptive control is based on a developed hybrid learning technique using an adaptive (on-line) learning rate for a Gaussian radial basis function neural network. The linear approach is used for a self-tuning pole-placement controller. A selective forgetting factor method is applied to both control schemes: in the neural case to estimate on-line the second-layer weights and in the linear case to estimate the parameters of the linear process model. These two techniques are applied to a laboratory-scaled bench plant with the possibility of dynamic changes and different types of disturbances. Experimental results show the superior performance of the neural approach particularly when there are dynamic changes in the process.

Experimental and simulation studies of multivariable adaptive optimization of continuous bioreactors using bilevel forgetting factors

A multivariable on-line adaptive optimization algorithm using a bilevel forgetting factor method was developed and applied to a continuous baker's yeast culture in simulation and experimental studies to maximize the cellular productivity by manipulating the dilution rate and the temperature. The algorithm showed a good optimization speed and a good adaptability and reoptimization capability. The algorithm was able to stably maintain the process around the optimum point for an extended period of time. Two cases were investigated: an unconstrained and a constrained optimization. In the constrained optimization the ethanol concentration was used as an index for the baking quality of yeast cells. An equality constraint with a quadratic penalty was imposed on the ethanol concentration to keep its level close to a hypothetical "optimum" value. The developed algorithm was experimentally applied to a baker's yeast culture to demonstrate its validity. Only unconstrained optimization was carried out experimentally. A set of tuning parameter values was suggested after evaluating the results from several experimental runs. With those tuning parameter values the optimization took 50-90 h. At the attained steady state the dilution rate was 0.310 h(-1) the temperature 32.8 degrees C, and the cellular productivity 1.50 g/L/h.

Recursive Synthetic Generalized Predictive Self-tuning Controller

Based on the Generalized Predictive Control (GPC) (Clarke, 1984a, 1984b) and the Recursive Generalized Predictive Self-tuning Controller (RGPC) (Yuan Zhu-zhi, 1986). A new self-tuning algorithm - Recursive Synthetic Generalized Predictive Self-tuning Controller (RSGPC) is advanced in this paper. By the addition of the design polynomials p(z-1), Q(z-1), T(z-1) and the feedforward compensation. It is developed into a useful self-tuning algorithm to the actual process. The recursion of inverting a matrix is used for saving the calculation time on-line as in the paper (Yuan Zhu-zhi, 1986) and the recursive squares root time-varying forgetting factor method is used to estimate the parameters for improving the precision. It makes RSGPC become a good adaptive controller to many plants. The simulation shows that RSGPC has a strong adaptation to the change of the dead-time, the model order and the nominimum-phase systems. The application of RSGPC in a paper machine shows further the good quality of this controller