Multiscale fuzzy Kalman filtering

Fuzzy Kalman filtering

New estimation methodologies for well logging problems via a combination of fuzzy Kalman filter and different smoothers

This paper proposes a new contaminant detection and water quality monitoring approach. Firstly, we propose an enhanced water quality modeling technique based on machine learning (e.g Gaussian process regression (GPR)) that aims at improving the proper understanding of the behavior of water distribution systems. To improve the performances of the developed water quality model even further, multiscale representation of data will be used to develop multiscale extension of these method. Multiscale representation is a powerful data analysis way that presents efficient separation of deterministic characteristics from random noise. Thus, multiscale GPR method, that combines the advantages of the machine learning method with those of multiscale representation, will be developed to enhance the water quality modeling performance. Secondly, technique to detect contaminant in WDN using hypothesis testing chart will be developed. Generalized likelihood ratio test (GLRT) has shown a good detection performances when compared to the classical detection charts. Then, to further enhance the performance of contaminant detection, a multiscale GPR-based exponentially weighted moving average (EWMA) GLRT (EWMA-GLRT) chart is developed. Therefore, this paper aims at enhancing the performances of contaminant monitoring using multiscale GPR-based GLRT and MSGPR-based EWMA-GLRT approaches.

Hyper-plane-shaped clustering (HPSC) has been demonstrated to be more effective in Takagi–Sugeno (T–S) fuzzy model identification compared to hyper-sphere-shaped clustering. Although some HPSC algorithms, based on type-2 fuzzy theory, have already been developed and have been demonstrated to have outstanding performance in T–S fuzzy modeling, mismatching of the traditional hyper-sphere-shaped membership function and HPSC results will inevitably restrict the modeling performance. In this paper, a modified inter type-2 fuzzy c-regression model (IT2-FCRM) clustering and new hyper-plane-shaped Gaussian membership function were proposed for T–S fuzzy modeling. In the proposed approach, the coefficients of the upper and lower hyperplanes were deduced based on an IT2-FCRM algorithm. Then, a hyper-plane-shaped membership function was directly defined using the hyperplanes to identify the antecedent parameters of the T–S fuzzy model. The experimental results of several benchmark problems show that identification of T–S model accuracy was greatly promoted.

In this study, the observation model of Kalman Filter (KF) is extended to an errors-in-variables (EIV) model because the observations may exist in the design matrix of the observation model. Then, a robust total least squares method (RTLS) is introduced into the KF, and a robust total Kalman filter (RTKF) algorithm is derived. The RTKF is a simple, flexible and effective algorithm. It is simple because its computational formulae are similar to the computational formulae of a standard KF; it is flexible because it can be used in a wide range of applications; it is effective because the influence of outliers on estimated results is weakened. Finally, the simulated example of the indoor location and the empirical example of pseudorange differential positioning are used to demonstrate the performance of the RTKF algorithm. The results prove the validity, robustness, and reliability of the RTKF in dealing with the outliers that exist in both observation vector and design matrix of the EIV model. Furthermore, the results of the empirical example show that the RTKF improves the precision of a pseudorange differential positioning compared with KF and robust Kalman filter (RKF) algorithms regardless the observation model has outliers or not in this empirical example.

A novel T-S fuzzy particle filtering algorithm based on fuzzy C-regression clustering

Optimizing a Kalman filter with an evolutionary algorithm for nonlinear quadrotor attitude dynamics

This paper proposes new algorithms based on the fuzzy c-regressing model algorithm for Takagi-Sugeno (T-S) fuzzy modeling of the complex nonlinear systems. A fuzzy c-regression state model (FCRSM) algorithm is a T-S fuzzy model in which the functional antecedent and the state-space-model-type consequent are considered with the available input-output data. The antecedent and consequent forms of the proposed FCRSM consists mainly of two advantages: one is that the FCRSM has low computation load due to only one input variable is considered in the antecedent part; another is that the unknown system can be modeled to not only the polynomial form but also the state-space form. Moreover, the FCRSM can be extended to FCRSM-ND and FCRSM-Free algorithms. An algorithm FCRSM-ND is presented to find the T-S fuzzy state-space model of the nonlinear system when the input-output data cannot be precollected and an assumed effective controller is available. In the practical applications, the mathematical model of controller may be hard to be obtained. In this case, an online tuning algorithm, FCRSM-FREE, is designed such that the parameters of a T-S fuzzy controller and the T-S fuzzy state model of an unknown system can be online tuned simultaneously. Four numerical simulations are given to demonstrate the effectiveness of the proposed approach.

The aim of this article is to establish generic stability conditions for switched nonlinear systems with mode-dependent average dwell-time (MDADT) switching rules via Takagi–Sugeno (T–S) fuzzy modeling, which cover all unstable modes, all stable modes, and partially unstable modes as special cases. Different from traditional multiple and multiple discontinuous Lyapunov function (MDLF) methods, the proposed novel switching-signal-based multiple discontinuous Lyapunov function (SMDLF) approach divides each mode-running interval dynamically according to the actual switching of the system. The developed approach can not only yield less conservative bounds on the MDADT but can also handle all unstable subsystems, which cannot be done by means of the traditional MDLF. A class of SMDLF is constructed for continuous-time switched T–S fuzzy systems, and relaxed stability conditions are presented for the system with both stable and unstable subsystems, using a larger switching signal space. Then, novel stability conditions are deduced for all stable and unstable subsystems in terms of slow and fast MDADT switching signals, respectively. Finally, comparative simulation examples are provided to verify the advantages and effectiveness of the proposed approach.

In Kalman filter design, the filter algorithm and prediction model design are the most discussed topics in research. Another fundamental but less investigated issue is the careful selection of measurands and their contribution to the estimation problem. This is often done purely on the basis of empirical values or by experiments. This paper presents a novel holistic method to design and assess Kalman filters in an automated way and to perform their analysis based on quantifiable parameters. The optimal filter parameters are computed with the help of a nonlinear optimization algorithm. To determine and analyze an optimal filter design, two novel quantitative nonlinear observability measures are presented along with a method to quantify the dominance contribution of a measurand to an estimate. As a result, different filter configurations can be specifically investigated and compared with respect to the selection of measurands and their influence on the estimation. An unscented Kalman filter algorithm is used to demonstrate the method’s capabilities to design and analyze the estimation problem parameters. For this purpose, an example of a vehicle state estimation with a focus on the tire-road friction coefficient is used, which represents a challenging problem for classical analysis and filter parameterization.

An adaptive Kalman filter algorithm is adopted to estimate the state of charge (SOC) of a lithium-ion battery for application in electric vehicles (EVs). Generally, the Kalman filter algorithm is selected to dynamically estimate the SOC. However, it easily causes divergence due to the uncertainty of the battery model and system noise. To obtain a better convergent and robust result, an adaptive Kalman filter algorithm that can greatly improve the dependence of the traditional filter algorithm on the battery model is employed. In this paper, the typical characteristics of the lithium-ion battery are analyzed by experiment, such as hysteresis, polarization, Coulomb efficiency, etc. In addition, an improved Thevenin battery model is achieved by adding an extra <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RC</i> branch to the Thevenin model, and model parameters are identified by using the extended Kalman filter (EKF) algorithm. Further, an adaptive EKF (AEKF) algorithm is adopted to the SOC estimation of the lithium-ion battery. Finally, the proposed method is evaluated by experiments with federal urban driving schedules. The proposed SOC estimation using AEKF is more accurate and reliable than that using EKF. The comparison shows that the maximum SOC estimation error decreases from 14.96% to 2.54% and that the mean SOC estimation error reduces from 3.19% to 1.06%.

This chapter investigates the problem of stabilization of nonlinear discrete-time networked control systems (NCS) with event-triggering communication scheme in the presence of signal transmission delay. A Takagi–Sugeno (T–S) fuzzy model and parallel-distributed compensation (PDC) scheme are first employed to design a nonlinear fuzzy event-triggered controller for the stabilization of nonlinear discrete-time NCS. The idea of the event-triggering communication scheme (a soft computation algorithm) under consideration is that the current sensor data is transmitted only when the current sensor data and the previously transmitted one satisfy a certain state-dependent trigger condition. By taking the signal transmission delay into consideration and using delay system approach, a T–S fuzzy delay system model is established to describe the nonlinear discrete-time NCSs with event-triggering communication scheme. Attention is focused on the design of fuzzy event-triggered controller which ensures asymptotic stability of the closed-loop fuzzy systems. Linear matrix inequality- (LMI-) based conditions are formulated for the existence of admissible fuzzy event-triggered controller. If these conditions are feasible, a desired fuzzy event-triggered controller can be readily constructed. A nonlinear mass-spring-damper mechanical system is presented to demonstrate the effectiveness of the proposed method.

Long term electric load forecasting based on TS-type recurrent fuzzy neural network model

The main method of modern ironmaking is blast furnace ironmaking, which is a very complex nonlinear dynamic process with complex physical-chemical coupling. The hot metal is the final product of blast furnace, and its silicon content not only reflects the quality of hot metal but also characterizes the operation status of the blast furnace, so its accurate prediction is very important for the operation of the blast furnace. Given the bottleneck problem in the application of the existing prediction model of hot metal silicon content in the blast furnace, this article proposed a novel data-driven modeling method. First, a nonlinear Takagi–Sugeno (T–S) fuzzy model is constructed for the hot metal silicon content to completely capture the nonlinear dynamics of the blast furnace process. Then, considering the doubts of blast furnace operators about the predicted results of the model, the Bayesian method is used to identify the consequent parameters of the fuzzy model to obtain the probability output, to present the credibility of the predicted results. Furthermore, to improve the robustness of the fuzzy model to the initial fuzzy rules, the sparse priori is adopted to construct a compact fuzzy model with strong generalization performance, in which the key fuzzy rules were screened out. In addition, two optimization methods are derived for each of the above models. Finally, the validity of the proposed methods is verified by the test of actual blast furnace data.

Electric vehicle battery management system works in the poor working environment, so that using conventional Kalman filtering algorithm to estimate the state of charge of electric vehicle battery will lead to inaccurate estimation, even divergent filtering. Aiming at the poor adaptive ability, defects of traditional filtering algorithm, the paper designs an improved fuzzy adaptive Kalman filter method, and applies it in the estimation of state of charge of electric vehicle battery. By monitoring the changes of residual online, the method uses the mean and the variance of the residual as the input of fuzzy controller, and adjusts the weight of the system noise and observation noise with fuzzy logic in real time, thus improves the estimation accuracy and realizes the optimal estimation of the filter. The simulation results show that this algorithm can predict the battery SOC effectively, and its accuracy is better than that of conventional Kalman filtering algorithm.