THE VALIDATION OF THE ROBUST INPUT ESTIMATION APPROACH TO TWO-DIMENSIONAL INVERSE HEAT CONDUCTION PROBLEMS

A novel adaptive and robust input estimation inverse methodology of estimating the time-varying unknown heat flux, named as the input, on the two active boundaries of a 2-D inverse heat conduction problem is presented. The algorithm includes using the Kalman filter to propose a regression model between the residual innovation and the two thermal unknown boundaries flux through given 2-D heat conduction state-space models and noisy measurement sequence. Based on this regression equation, a recursive least-square estimator (RLSE) weighted by the forgetting factor is proposed to on-line estimate these unknowns. The adaptive and robust weighting technique is essential since unknowns input are time-varied and have unpredictable changing status. In this article, we provide the bandwidth analysis together with bias and variance tests to construct an efficient and robust forgetting factor as the ratio between the standard deviation of measurement and observable bias innovation at each time step. Herein, the unknowns are robustly and adaptively estimated under the system involving measurement noise, process error, and unpredictable change status of time-varying unknowns. The capabilities of the proposed algorithm are demonstrated through the comparison with the conventional input estimation algorithm and validated by two benchmark performance tests in 2-D cases. Results show that the proposed algorithm not only exhibits superior robust capability but also enhances the estimation performance and highly facilitates practical implementation.     

INVERSE PROBLEM OF ESTIMATING INTERFACE CONDUCTANCE BETWEEN PERIODICALLY CONTACTING SURFACES USING THE WEIGHTING INPUT ESTIMATION METHOD

This work applied an on-line inverse solution methodology based on the weighting input estimation method to determine the interface contact conductance between periodically contacting surfaces. This method is based on the Kalman filtering technique and a recursive least-squares estimator. This recursive least-squares estimator is weighted by the forgetting factor n and proposed for extracting the unknowns. The weighting technique is essential, since the unknown input is time-varied and has an unpredictable changing status. The superior capabilities of this inverse method are demonstrated in several one-dimension timevarying estimate cases and the proposed algorithm is compared with the conjugate gradient method. Results show that this method has the advantages of stability, fast convergence, good accuracy, and demonstrates that only a few measurement sensors are needed.     

Estimation of time-dependent heat flux and measurement bias in two-dimensional inverse heat conduction problems

This paper presents the results from the adaptive estimator developed to estimate time-dependent boundary heat flux in two-dimensional heat conduction domain with heated and insulated walls. For the estimation, the algorithm requires only the temperatures measured at the insulated walls. In addition, the estimator also predicts the bias in the measurements. In modeling the system, it is assumed that the input flux and bias sequence dynamics can be modeled by a semi-Markov process. By incorporating the semi-Markovian concept into a Bayesian estimation technique, the estimator consists of a bank of parallel, adaptively weighted, Kalman filters. Computer simulation results reveal that the proposed adaptive estimator has improved estimation performance even for step changing heat flux and measurement bias.     

SOC estimation of lithium battery based on adaptive untracked Kalman filter

电池荷电状态（SOC）的准确估计是电池管理系统的关键问题,对电池的可靠性和安全性至关重要。由于多数情况下建立的电池模型精度不够高、电池系统的噪声统计是未知的或不准确的,这都会对锂离子电池系统的SOC估计会产生较大影响。本文采用二阶RC等效模型,可减小电池模型带来的误差;同时结合SageHusa滤波算法与无迹卡尔曼滤波（UKF）算法提出了一种新的SOC估计方法,基于噪声统计估计器的自适应无迹卡尔曼（AUKF）滤波算法,它可以对系统噪声进行实时修正以提高SOC的估算精度。并通过比较AUKF和UKF来验证SOC估计方法的准确性和有效性。实验结果表明,AUKF具有更高的SOC估计精度和自适应能力,在脉冲放电工况和动态工况下的估计精度均能保持在4.68%以内,可以有效地估计电池的SOC值。     

Inverse estimation of heat flux and temperature in multi-layer gun barrel

In this paper, we present an inverse method, an input estimation method, to recursively estimate both the time varied heat flux and the inner wall temperature in the chamber. The algorithm includes the use of the Kalman filter to derive a regression model between the biased residual innovation and the heat flux through a given heat conduction state space model. Based on this regression model, the Recursive Least Squares Estimator (RLSE) is proposed to extract the time-varying heat flux on-line as the input. Computational results show that the proposed method exhibits a good estimation performance and highly facilitates practical implementation.     

State of charge estimation method based on the extended Kalman filter algorithm with consideration of time-varying battery parameters

In developing battery management systems, estimating state-of-charge (SOC) is important yet challenging. Compared with traditional SOC estimation methods (eg, the ampere-hour integration method), extended Kalman filter (EKF) algorithm does not depend on the initial value of SOC and has no accumulated error, which is suitable for the actual working condition of electric vehicles. EKF is a model-based algorithm; the accuracy of SOC estimated by this algorithm was greatly influenced by the accuracy of battery model and model parameters. The parameters of battery change with many factors and exhibit strong nonlinearity and time variance. Typical EKF algorithm approximates battery as a linear, time-invariant system; however, this approach introduces estimation errors. To minimize such errors, previous studies have focused on improving the accuracy of identifying battery parameters. Although studies on battery model with time-varying parameters have been carried out, few have studied the combination of time-varying battery parameters and EKF algorithm. A SOC estimation method that combines time-varying battery parameters with EKF algorithm is proposed to improve the accuracy of SOC estimation. Battery parameter data were obtained experimentally under different temperatures, SOC levels, and discharge rates. The results of parameter identification are made into a data table, and the battery parameters in the EKF system matrix are updated by looking up the data in the table. Simulation and experimental results shown that, average error of SOC estimated by the proposed algorithm is 2.39% under 0.9 C constant current discharge and 2.4% under 1.3 C, which is 1.91% and 2.35% lower than that of EKF algorithm with fixed battery parameters. Under intermittent discharge with constant current (1.1 C) and capacity (10%), the average error of SOC estimated by the proposed algorithm is 1.4%, which is 0.3% lower than that of EKF algorithm with fixed battery parameters. The average error of SOC estimated by the proposed algorithm under the New European Driving Cycle (NEDC) is 1.6%, which is 0.2% lower than that of EKF algorithm with fixed battery parameters. Relative to the EKF algorithm with fixed battery parameters, the proposed EFK algorithm with time-varying battery parameters yields higher accuracy.     

Fractional‐order modeling and SOC estimation of lithium‐ion battery considering capacity loss

For state‐of‐charge (SOC) estimation, the resistance deterioration and continuous capacity loss can lead to erroneous estimation results. In this paper, an SOC estimator of lithium‐ion battery based on the fractional‐order model and adaptive dual Kalman filtering algorithm is proposed first. Then, to improve the accuracy of SOC estimation considering capacity loss, the particle filter algorithm is applied to update capacity online in real time. Then, an SOC estimation method is proposed considering battery capacity loss. The simulation results show that the accuracy of battery capacity prediction based on particle filter is high under the condition of capacity loss.     

A modified neural learning algorithm for online rotor resistance estimation in vector controlled induction motor drives

Online estimation of rotor resistance is essential for high performance vector controlled drives. In this paper, a novel modified neural algorithm has been identified for the online estimation of rotor resistance. Neural based estimators are now receiving active consideration as they have a number of advantages over conventional techniques. The training algorithm of the neural network determines its learning speed, stability, weight convergence, accuracy of estimation, speed of tracking and ease of implementation. In this paper, the neural estimator has been studied with conventional and proposed learning algorithms. The sensitivity of the rotor resistance change has been tested for a wide range of variation from -50% to+50% on the stability of the drive system with and without estimator. It is quiet appealing to settle with optimal estimation time and error for the viable realization. The study is conducted extensively for estimation and tracking. The proposed learning algorithm is found to exhibit good estimation and tracking capabilities. Besides, it reduces computational complexity and, hence, more feasible for practical digital implementation.     

A wavelet transform‐adaptive unscented Kalman filter approach for state of charge estimation of LiFePo4 battery

LiFePo₄ battery is widely used in electric vehicles; however, its flatness and hysteresis of the open‐circuit voltage curve pose a big challenge to precise state of charge (SOC) estimation. The issue is discussed and addressed in this paper. First, a cell model with hysteresis is built to describe real‐time dynamic characteristics of the LiFePo₄ battery. Second, the model parameters and SOC are estimated independently to avoid the possibility of cross interference between them. For model identification, an adaptive unscented Kalman filter (AUKF) algorithm is used to identify the cell parameters as they change slowly. While SOC could change rapidly, wavelet transform AUKF algorithm is put forward to estimate SOC. In the novel algorithm, the measurement noise can be estimated and updated online. Finally, the performance of the proposed method is verified under dynamic current condition. The experimental results show that estimated value based on the proposed method is more accurate than unscented Kalman filter‐based method and AUKF‐based algorithm. Meanwhile, the proposed estimator also has the merits of fast convergence and good robustness against the initialization uncertainty.     

State of charge estimation for lithium-ion battery based on an intelligent adaptive unscented Kalman filter

Adaptive unscented Kalman filter (AUKF) has been widely used for state of charge (SOC) estimation of lithium-ion battery. The noise covariance of the conventional AUKF method is updated based on the innovation covariance matrix (ICM), which is estimated using the error innovation sequence (EIS). However, the distribution of EIS changes due to the time-varying noise, load current dynamics and modelling error, which will lead to inaccurate ICM estimation. Therefore, an intelligent adaptive unscented Kalman filter (IAUKF) method is proposed to detect the distribution change of EIS. Then, the ICM is estimated based on the EIS after the distribution change. Results show that the IAUKF method can improve SOC estimation accuracy significantly. Compared with that of the AUKF method, the root mean squared error and the mean absolute error of SOC based on the IAUKF method decrease by 43.70% and 72.37% under random walk discharge condition, respectively. In addition, the computation time of the IAUKF method slightly increases by 6.27% compared with that of AUKF method. Finally, the effect of initial parameters on the SOC estimation accuracy was analysed. The results indicate that proper algorithm tuning, such as initial window length of EIS for ICM update and the threshold value, can further improve the SOC accuracy based on the proposed IAUKF method. The proposed IAUKF method also shows high robustness against initial measurement noise covariance.     

A model‐based and data‐driven joint method for state‐of‐health estimation of lithium‐ion battery in electric vehicles

Lithium‐ion battery state‐of‐health estimation is one of the vital issues for electric vehicle safety. In this work, a joint model‐based and data‐driven estimator is developed to achieve accurate and reliable state‐of‐health estimation. In the estimator, an increase in ohmic resistance extracted from the Thevenin model is defined as the health indicator to quantify the capacity degradation. Then, a linear state‐space representation is constructed based on the data‐driven linear regression. Furthermore, the Kalman filter is introduced to trace capacity degradation based on the novel state space representation. A series of battery aging datasets with different dynamic loading profiles and temperatures are obtained to demonstrate the accuracy and robustness of the proposed method. Results show that the maximum error of the Kalman filter is 2.12% at different temperatures, which proves the effectiveness of the proposed method.     

Unbalanced transients-based maximum likelihood identification of induction machine parameters

The paper describes an effective formulation of a maximum-likelihood identification algorithm for linear estimation of the equivalent-circuit parameters of cage-type (single cage and double cage) or deep-bar induction motors with measurement and process noises. A complete generalized model for symmetrical and asymmetrical test analysis of induction machines is developed for this purpose. The paper outlines the theory and reasoning behind the proposed statistical-based treatment of online data derived from generalized least-squares estimator and a Kalman filter. The method is successfully applied to online double-line independent finite-element (FE) short-circuit-simulated records of a deep-bar-type induction motor.     

Nonlinear optimal on-line heat-dissipation control methodology in electronic devices

The essential element in obtaining semiconductor electronic device enhanced reliability involves solving the heat-dissipating issue. Certain electronic components possess varying thermal properties and the strength of the heat generated by the semiconductor chip is unknown. Therefore, the heat dissipation control problem is both complicated and perplexing. This paper proposes a methodology, the LQG/IE tracking algorithm, to solve the nonlinear heat dissipation control problem. The IE method, which is a combination of an Extended Kalman filter and Recursive Least Squares Estimator, estimates (in real time) the unknown time-varying heat source generated by the semiconductor chip using temperature measurements of the package seal surface. The LQG tracking algorithm is adopted to analyze the feedback gain to control the heat dissipation. The simulation results reveal that an effective and optimal heat dissipation controller can be implemented for the cooling system using the LQG/IE tracking algorithm.     

State‐of‐charge estimators considering temperature effect,hysteresis potential,and thermal evolution for LiFePO4 batteries

To achieve accurate state‐of‐charge (SoC) estimation for LiFePO₄ batteries, the effects of temperature, hysteresis, and thermal evolution are elaborately modeled. Open‐circuit voltage is regarded as the sum of electromotive force and hysteresis potential (V_h), where electromotive force is constructed as the function of SoC and temperature and V_h is reproduced with a geometrical model. By simulating battery heat generation and dissipation, a thermal evolution model is established and exploited for open‐circuit voltage and parameter identification. Then, on the basis of a second‐order equivalent circuit model, 2 SoC estimation schemes are proposed: One scheme uses the recursive least square with forgetting factor algorithm and off‐line equivalent circuit model parameters derived by the differential evolution algorithm; the other scheme resorts to the adaptive extended Kalman filter (EKF) and online tuned parameters. Experiments validate the effectiveness of the hysteresis model and the thermal evolution model. In contrast to a joint EKF estimator, experimental results under different temperatures and initial states suggest that both the proposed estimators are superior to the joint EKF estimator. Benefiting from the online updated parameters, the adaptive EKF estimator behaves best for giving consistent SoC‐tracking performance under different conditions.     

Adaptive fuzzy sliding-mode control for induction servomotor systems

An adaptive fuzzy sliding-mode control design method is proposed for induction servomotor system control. The proposed adaptive fuzzy sliding-mode control system is comprised of a fuzzy controller and a compensation controller. The fuzzy controller is the main tracking controller, which is used to approximate an ideal computational controller. The compensation controller is designed to compensate for the difference between the ideal computational controller and the fuzzy controller. A tuning methodology is derived to tune the premise and consequence parts of the fuzzy rules. The online tuning algorithm is derived in the Lyapunov sense; thus, the stability of the control system can be guaranteed. Moreover, to relax the requirement for the uncertain bound in the compensation controller, an estimation mechanism is investigated to observe the uncertain bound, so that the chattering phenomena of the control efforts can be relaxed. To illustrate the effectiveness of the proposed design method, a comparison between a conventional fuzzy control and the proposed adaptive fuzzy sliding-mode control is made. Simulation and experimental results verify that the proposed adaptive fuzzy sliding-mode control design method can achieve favorable control performance with regard to parameter variations and external disturbances.     

2001 Middle-East Power Systems Conference 29-31 December 2001 Helwan, Cairo, Egypt

This letter presents a method for induction motor on-line rotor resistance estimation. This is important in vector control, if high-performance torque control is needed. For this purpose, a fuzzy logic technique is used to estimate the rotor resistance. The fuzzy estimator (FE) principle design is then presented, and simulations demonstrate the effectiveness of the proposed method.     

电站锅炉声学测温中时延估计试验研究

对锅炉炉膛冷态和热态声场进行了分析,从理论上对广义互相关时延估计及其加权函数进行了深入探讨,并在国内某300MW机组上安装声学测点,对不同的加权函数进行了冷态和热态试验研究.结果表明：广义互相关时延估计法可以用于声学测温中声波飞渡时间的测量;PHAT加权具有抗混响能力,能在锅炉冷态混响环境下得到准确的时延估计;ML加权具有很好的抗噪能力,能在锅炉热态时得到准确的声波飞渡时间.     

Fast inverse prediction of phase change banks in high temperature furnaces with a Kalman filter coupled with a recursive least-square estimator

An inverse heat transfer procedure for predicting the time-varying thickness of phase-change banks on the inside surface of the walls of high temperature furnaces is presented. The main feature of the inverse method is its unique capability of making fast predictions so that it can be easily integrated to existing real-time control systems of industrial facilities. The method rests on fast computing state-space models (direct model) that are designed to mimic the response of a full finite-difference model of the phase change problem. A Kalman filter coupled with a recursive least-square estimator (inverse method) is employed to estimate the time-varying phase front position from the data collected by a temperature and/or heat flux sensor located in the furnace wall. The inverse heat transfer procedure is thoroughly tested for typical phase change conditions that prevail inside industrial facilities. The effect of the sensor type (temperature sensor or heat flux sensor), of its location and of the measurement noise on the accuracy and stability of the predicted bank thickness is investigated. It is shown that the proposed inverse heat transfer procedure becomes increasingly reliable and accurate for predicting the bank thickness as it shrinks. This feature is of the utmost interest for preventing the sudden and accidental loss of the protective banks of industrial furnaces filled with molten material. Recommendations are also made concerning the type and location of sensors.     

Developing a multipurpose sun tracking system using fuzzy control

The present work demonstrates the design and simulation of time controlled step sun tracking systems that include: one axis sun tracking with the tilted aperture equal to the latitude angle, equatorial two axis sun tracking and azimuth/elevation sun tracking. The first order Sugeno fuzzy inference system is utilized for modeling and controller design. In addition, an estimation of the insolation incident on a two axis sun tracking system is determined by fuzzy IF-THEN rules. The approach starts by generating the input/output data. Then, the subtractive clustering algorithm, along with least square estimation (LSE), generates the fuzzy rules that describe the relationship between the input/output data of solar angles that change with time. The fuzzy rules are tuned by an adaptive neuro-fuzzy inference system (ANFIS). Finally, an open loop control system is designed for each of the previous types of sun tracking systems. The results are shown using simulation and virtual reality. The site of application is chosen at Amman, Jordan (32° North, 36° East), and the period of controlling and simulating each type of tracking system is the year 2003.     

Real‐time thermal states monitoring of absorber tube for parabolic trough solar collector with non‐uniform solar flux

With the world energy shortage problem becoming increasingly prominent, more and more attentions have been paid to the development of renewable energies. Among these sources, solar energy has received extensive attention with its excellent characteristics. The thermal state affects the safety of the solar heat collection system. In this paper, real‐time monitoring of the input heat flux on the inside wall and the temperature field simultaneously of an absorber tube for parabolic trough solar collector were studied. Based on the measured temperatures on the outside wall, the fuzzy adaptive Kalman filter coupled with weighted recursive least squares algorithm (WRLSA) was employed to monitor the heat states of the absorber tube inversely, in which WRLSA was used to acquire the heat flux while fuzzy adaptive Kalman filter was adopted to monitor the temperature field. The method showed strong robustness to resist the ill‐posedness. Accurate monitoring results also can be acquired when there are random disturbances of the heat transfer condition on the inner wall.