应用DEKF算法训练模糊化神经网络

模糊MLP网络的待定参数规模比确定性MLP网络的多几倍，急需找到高效的训练算法。本文尝试用DEKF训练模糊神经网络，这是DEKF算法新的应用。仿真表明，DEKF算法比经典BP算法的收敛速度更快，训练所得网络的精度更高。     

State of charge estimation for lithium-ion batteries based on adaptive dual Kalman filter

Accurate estimation of the battery state of charge (SOC) is of great significance for enhancing its service life and safety. In this study, based on the fractional-order equivalent circuit model of lithium-ion battery, the SOC estimation methods using dual Kalman filter (DKF) and dual extended Kalman filter (DEKF) are simulated and compared, in terms of model accuracy and SOC estimation accuracy. Then, combining the advantages of the DKF and DEKF algorithms, an SOC estimation algorithm based on adaptive double Kalman filter is proposed. This algorithm uses the recursive least squares (RLS) method to update the battery model parameters online in real time, and employs the DKF algorithm to filter the SOC twice to reduce the interferences from the battery model error and the current measurement error. In the experimental studies, the measured SOC values are compared with the estimated SOC values produced by the proposed algorithm. The comparison results show that SOC estimation error of the proposed algorithm is within the range of ±0.01 under most test conditions, and it can automatically correct SOC to true value in the presence of system errors. Thus, the validity, accuracy, robustness and adaptability of the proposed algorithm under different operation conditions are verified.     

Control of a twin clutch transmission for smooth gearshifts

The flow of torque in a twin clutch transmission is investigated and the different phases of torque transfer between the two clutches are studied. In order to prevent torque backlash and intense wear in dry clutch plates, a proper clamp force regulation is used. A full vehicle simulation that includes vehicle and powertrain components is set up. A Fuzzy logic control system is found suitable for clamp force and engine throttle controls. For upshift and downshift cases, the design of controllers for the gearshift process is carried out by defining proper membership functions and Fuzzy rules using Matlab/Simulink^TM software. The effectiveness of the control system is investigated by simulating two upshift and downshift cases. Results indicate that the control system is successful in regulating the clutch clamp forces and the engine throttle in such a way that a smooth torque flow in the transmission is achieved in all cases.     

Extended Kalman filters using explicit and derivative-free local linearizations

We propose three variants of the extended Kalman filter (EKF) especially suited for parameter estimations in mechanical oscillators under Gaussian white noises. These filters are based on three versions of explicit and derivative-free local linearizations (DLL) of the non-linear drift terms in the governing stochastic differential equations (SDE-s). Besides a basic linearization of the non-linear drift functions via one-term replacements, linearizations using replacements through explicit Euler and Newmark expansions are also attempted in order to ensure higher closeness of true solutions with the linearized ones. Thus, unlike the conventional EKF, the proposed filters do not need computing derivatives (tangent matrices) at any stage. The measurements are synthetically generated by corrupting with noise the numerical solutions of the SDE-s through implicit versions of these linearizations. In order to demonstrate the effectiveness and accuracy of the proposed methods vis-à-vis the conventional EKF, numerical illustrations are provided for a few single degree-of-freedom (DOF) oscillators and a three-DOF shear frame with constant parameters.     

The extended Kalman Filter and the unscented Kalman Filter for Material Parameter Identification with Application in Tunneling

We present in this work the use of the extended Kalman filter (EKF) and unscented Kalman filter (UKF) for identification of constitutive material parameters with application in mechanized tunneling. Although both filters are based on the principle of recursive least squares estimation, one differs from another in terms of where approximation is made. Whereas in the EKF first-order Taylor series expansion is used to approximate the nonlinear modeling equation, in the UKF approximation of the probability density of the state is made using a small number of well defined points. To validate the methods, we performed parameter identification of the Hardening Soil constitutive model used for describing the soil behavior in an tunnel excavation model. Both methods showed fast and stable convergence of the considered soil parameters - the four parameters of the Hardening Soil model. Although the EKF requires less number of forward calculations of the numerical model, the UKF is favored since it does not require calculation of the derivatives of the observables with respect to the identifying parameters. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

New approach to applying neural network in nonlinear dynamic model

In this work, radial basis function neural network (RBF-NN) is applied to emulate an extended Kalman filter (EKF) in a data assimilation scenario. The dynamical model studied here is based on the one-dimensional shallow water equation DYNAMO-1D. This code is simple when compared with an operational primitive equation models for numerical weather prediction. Although simple, the DYNAMO-1D is rich for representing some atmospheric motions, such as Rossby and gravity waves. It has been shown in the literature that the ability of the EKF to track nonlinear models depends on the frequency and accuracy of the observations and model errors. In some cases, just fourth-order moment EKF works well, but will be unwieldy when applied to high-dimensional state space. Artificial Neural Network (ANN) is an alternative solution for this computational complexity problem, once the ANN is trained offline with a high order Kalman filter, even though this Kalman filter has high computational cost (which is not a problem during ANN training phase). The results achieved in this work encourage us to apply this technique on operational model. However, it is not yet possible to assure convergence in high dimensional problems.     

Extended-Kalman-filter-based chaotic communication

Together with the optimal linearization technique, an extended-Kalman-filter-basedchaotic communication is first proposed in this paper. First,the optimal linearization technique is utilized to find theexact linear models of the chaotic system at operating statesof interest. Then, an extended Kalman filter (EKF) algorithmis used to estimate both the parameters and states where themessage is already embedded. By using the EKF together withthe optimal linear model, the message can be recovered wellat the receiver's end. Numerical examples and simulations aregiven to show the effectiveness of the proposed methodology.     

Nonlinear continuous-discrete filtering using kernel density estimatesand functional integrals

We develop filter algorithms for nonlinear stochastic differential equations with discrete time measurements (continuous-discrete state space model). The apriori density (time update) is computed by Monte Carlo simulations of the Fokker-Planck equation using kernel density estimators and measurement updates are obtained by using the extended Kalman filter (EKF) updates. For small sampling intervals, a discretized continuous sampling approach (DCS) is used. A third algorithm utilizes a functional (path) integral representation of the transition density (functional integral filter FIF). The kernel density filter (KDF), DCS, and FIF are compared with the EKF and the Gaussian sum filter by using a Ginzburg-Landau-equation and a stochastic volatility model.     

A chaos secure communication scheme based on multiplication modulation

A secure spread spectrum communication scheme using multiplication modulation is proposed. The proposed system multiplies the message by chaotic signal. The scheme does not need to know the initial condition of the chaotic signals and the receiver is based on an extended Kalman filter (EKF). This signal encryption scheme lends itself to cheap implementation and can therefore be used effectively for ensuring security and privacy in commercial consumer electronics products. To illustrate the effectiveness of the proposed scheme, a numerical example based on Genesio-Tesi system and also Chen dynamical system is presented and the results are compared.     

Parameter Estimation of Nonlinear Stochastic Differential Equations: Simulated Maximum Likelihood versus Extended Kalman Filter and Itô-Taylor Expansion

This article compares several estimation methods for nonlinear stochastic differential equations with discrete time measurements. The likelihood function is computed by Monte Carlo simulations of the transition probability (simulated maximum likelihood SML) using kernel density estimators and functional integrals and by using the extended Kalman filter (EKF and second-order nonlinear filter SNF). The relation with a local linearization method is discussed. A simulation study for a diffusion process in a double well potential (Ginzburg–Landau equation) shows that, for large sampling intervals, the SML methods lead to better estimation results than the likelihood approach via EKF and SNF. A second study using a nonlinear diffusion coefficient (generalized Cox–Ingersoll–Ross model) demonstrates that the EKF type estimators may serve as efficient alternatives to simple maximum quasilikelihood approaches and Monte Carlo methods.     

System Identification based on Model Synchronization

Detailed knowledge about system parameters is required in many technical applications in order to model the system adequately. The question how to obtain parameter values and state maps of certain components thus is of significant importance in engineering applications. In this contribution, a novel approach to identifying system parameters and parameter-free state maps of a simple nonlinear clutch actuation device is presented. To identify parameters, the Extended Kalman Filter (EKF) is used for synchronizing a system model with measurements of the system response to transient excitation. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Adaptive Estimation of FCG Using Nonlinear State-Space Models

Abstract

In this paper, an efficient adaptive nonlinear algorithm for estimation and identification, the so-called adaptive Lainiotis filter (ALF), is applied to the problem of fatigue crack growth (FCG) estimation, identification, and prediction of the final crack (failure). A suitable nonlinear state-space FCG model is introduced for both ALF and extended Kalman filter (EKF). Both algorithms are tested in order to compare their efficiency. Through extensive analysis and simulation, it is demonstrated that the ALF has superior performance both in FCG estimation, as well as in predicting the remaining lifetime to failure. Furthermore, it is shown that the ALF is faster and easier to implement in a parallel/distributed processing mode, and much more robust than the classic EKF.     

Active Disturbance Rejection Control of Quadrotor UAVs Based on Joint Observation and Feedforward Compensation北大核心CSCD

为解决模型参数不确定与外界干扰影响下,四旋翼无人机飞控作业中姿态与轨迹跟踪精度下降,反应迟缓的问题,利用拓展Kalman滤波应对非线性系统问题出色的适应能力和噪声抑制能力,对四旋翼状态信息进行初步估算来抑制高频信号干扰,从而降低了扩张状态观测器的估计负担.同时,与扩张状态观测器联合估计由系统不确定性参数与外界扰动联合组成的“总扰动”,使系统对于精确模型的依赖性降低,并利用扰动估计的微分值进行前馈补偿,以提高对突变扰动的跟踪精度,克服了突变干扰下的相位滞后现象.综合联合观测器、带前馈补偿的LESO及带误差补偿的PD控制律,形成了一种利用拓展Kalman滤波与前馈补偿后的扩张状态观测器联合观测扰动,能较大程度抑制高频噪声和突变扰动的改进型自抗扰控制器.仿真与实验结果表明,联合观测器能有效地减小观测误差幅值且能超前校正观测相位滞后,从而更好地得到更精确的状态信息,改进型自抗扰控制器能更好地满足四旋翼飞行器快速反应、高效稳定的控制要求,精准高效地完成复杂轨迹跟踪.     

Time-Varying Parameters Prediction

This paper develops a method of adaptive modeling that may be applied to forecast non-stationary time series. The starting point are time-varying coefficients models introduced in statistics, econometrics and engineering. The basic step of modeling is represented by the implementation of adaptive recursive estimators for tracking parameters. This is achieved by unifying basic algorithms—such as recursive least squares (RLS) and extended Kalman filter (EKF)—into a general scheme and next by selecting its coefficients with the minimization of the sum of squared prediction errors. This defines a non-linear estimation problem that may be analyzed in the context of the conditional least squares (CLS) theory. A numerical application on the IBM stock price series of Box-Jenkins illustrates the method and shows its good forecasting ability.     

An exact minimum variance filter for a class of discrete time systems with random parameter perturbations

An exact, closed-form minimum variance filter is designed for a class of discrete time uncertain systems which allows for both multiplicative and additive noise sources. The multiplicative noise model includes a popular class of models (Cox-Ingersoll-Ross type models) in econometrics. The parameters of the system under consideration which describe the state transition are assumed to be subject to stochastic uncertainties. The problem addressed is the design of a filter that minimizes the trace of the estimation error variance. Sensitivity of the new filter to the size of parameter uncertainty, in terms of the variance of parameter perturbations, is also considered. We refer to the new filter as the ‘perturbed Kalman filter’ (PKF) since it reduces to the traditional (or unperturbed) Kalman filter as the size of stochastic perturbation approaches zero. We also consider a related approximate filtering heuristic for univariate time series and we refer to filter based on this heuristic as approximate perturbed Kalman filter (APKF). We test the performance of our new filters on three simulated numerical examples and compare the results with unperturbed Kalman filter that ignores the uncertainty in the transition equation. Through numerical examples, PKF and APKF are shown to outperform the traditional (or unperturbed) Kalman filter in terms of the size of the estimation error when stochastic uncertainties are present, even when the size of stochastic uncertainty is inaccurately identified.     

On the fractional-order extended Kalman filter and its application to chaotic cryptography in noisy environment

In this paper via a novel method of discretized continuous-time Kalman filter, the problem of synchronization and cryptography in fractional-order systems has been investigated in presence of noisy environment for process and output signals. The fractional-order Kalman filter equation, applicable for linear systems, and its extension called the extended Kalman filter, which can be used for nonlinear systems, are derived. The result is utilized for chaos synchronization with the aim of cryptography while the transmitter system is fractional-order, and both the transmitter and transmission channel are noisy. The fractional-order stochastic chaotic Chen system is then presented to apply the proposed method for chaotic signal cryptography. The results show the effectiveness of the proposed method.     

Integrated Motional Measurement for a Flexible Structure

Integrated navigation systems based on gyros and accelerometers are well established devices for vehicle guidance. The system design is traditionally based on the assumption that the vehicle is a rigid body. However, generalizing such integrated systems to flexible structures is possible. The example of the motion of a simple beam being considered here is meant to be a first approach to obtain sophisticated motional measurements of a wing of a large airplane during flight. The principle of integrated navigation systems consists of combining different measuring methods by using their specific advantages. Gyros and accelerometers are used to obtain reliable signals within a short period of time. On the other hand, aiding sensors like radar units and strain gauges are used because of their long-term accuracy. The kernel of the integrated system consists, however, of an extended Kalman filter that estimates the motion state of the structure. Besides the sensor signals, the basis for the filter is an additional kinematical model of the structure. By means of a model reduction, a kinematical model of the beam was developed. Based on simulation the paper presents this approach, the appropriate sensor set, and first estimated motion results. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An application of Chen system for secure chaotic communication based on extended Kalman filter and multi-shift cipher algorithm

In recent years chaotic secure communication and chaos synchronization have received ever increasing attention. In this paper a chaotic communication method using extended Kalman filter is presented. The chaotic synchronization is implemented by EKF design in the presence of channel additive noise and processing noise. Encoding chaotic communication is used to achieve a satisfactory, typical secure communication scheme. In the proposed system, a multi-shift cipher algorithm is also used to enhance the security and the key cipher is chosen as one of the chaos states. The key estimate is employed to recover the primary data. To illustrate the effectiveness of the proposed scheme, a numerical example based on Chen dynamical system is presented and the results are compared to two other chaotic systems.     

Integrated measurement system using accelerometers and gyros as peripheral sensors to estimate the motional state of an elastic beam

Integrated navigation devices for vehicle guidance are the most common example of an integrated motion measurement system combining the signals from an inertial measurement unit (IMU consisting of three accelerometers and three gyros) and a GPS receiver with a single antenna. For this, the vehicle is traditionally assumed to be a single rigid body with six motional degrees of freedom to be determined. During periods of low vehicle dynamics the common integrated navigation systems show, however, stability problems. Nevertheless, the stability of the system can be guaranteed by distributing sensors over the vehicle structure. In this case the rigid body assumption has to be expanded to take the distributed sensors and the flexibility of the structure into account. Integrated systems in general are fusing different measuring signals by combining their benefits and blinding out their disadvantages. For instance, gyros and accelerometers are used to obtain reliable signals with a good time resolution. On the other hand, aiding sensors like radar units and strain gauges are known to be long-term accurate. Furthermore, the kernel of such integrated systems consists of an extended Kalman filter that estimates the motion state of the structure. Besides the sensor signals, the basis for the filter is an additional kinematical model of the structure which has to be developed individually. The example of the motion of an elastic beam being considered here is meant to be an approach to obtain motional measurements of a wing of a large airplane during flight. By means of a modal approach, a kinematical model of the beam was developed. This paper will compare integrated systems utilising accelerometers as peripheral sensors with systems using gyros and systems with a combination of both peripheral sensor types. Based on simulation the paper shows this approach, different sensor configurations, and estimated motion results of an elastic beam. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear dynamic effects in automotive clutches

Dynamic effects appearing in the dry friction clutches are very complex. The reason for this is the usual design of the clutches including complex two dimensional friction, unilateral contacts and nonlinear springs. The final quality of the clutch system for a customer depends among other criteria on the awareness of dynamic effects, which can affect functioning and comfort negatively. One of the usual nonlinear dynamic effects in the friction clutch is presented in this work. That is the problem of dynamic disengagement which can cause significant safety problems. First of all the global nonlinear dynamic behavior is considered roughly by means of an analytical approach. Secondly a MBS-model, which includes not only the nominal design of the clutch system but also dispersion of several parameters, is used in order to identify the influence of the asymmetry on the dynamic behavior. Analytical and numerical results are compared with measurements. Finally a possible solution of the considered problem is presented. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)