Recursive Parameter Estimation Method Research Articles

Real-time coordinated control strategy for the hybrid electric propulsion system of a flying car with model adaptation and game theory

Coordination among the multiple power components is essential for the hybrid electric propulsion systems since the decision made by one impacts the state and decisions of others due to the coupling mechanical and electrical dynamics. Traditional model-based approaches with weight-sum objectives may result in misleading optimization or even unstable situations because of the inherent poor scalability and synergy. To overcome this issue, this paper proposes a novel game theory-based control strategy with model adaptation mechanism for the hybrid electric flying car to enhance the control performance, system stability, and robustness. Firstly, a control-oriented model of the system is derived with the utilization of the recursive least square parameter estimation method. The non-cooperative game framework is then established with the turboshaft engine subsystem and electric supply subsystem treated as two independent players. The performance of Nash equilibrium solutions with closed-loop and open-loop information structures are investigated where the problem is iteratively solved by exploiting Pontryagin’s Minimum Principle and dynamic programming, respectively. The simulation results demonstrate that the game theory-based controllers can outperform MPC with the weight-sum objectives in terms of control efficiency and robustness improvement and the game theory-based controller with open-loop information structure shows excellent computation efficiency. Moreover, the result of the hardware-in-the-loop experiment demonstrates the real-time performance of the proposed controller.

Sensor Based System Identification in Real Time for Noise Covariance Deficient Models

System identification methods have extensive application in the aerospace industry’s experimental stability and control studies. Accurate aerodynamic modeling and system identification are necessary because they enable performance evaluation, flight simulation, control system design, fault detection, and model aircraft’s complex non-linear behavior. Various estimation methods yield different levels of accuracies with varying complexity and computational time requirements. The primary motivation of such studies is the accurate quantification of process noise. This research evaluates the performance of two recursive parameter estimation methods, viz.; First is the Fourier Transform Regression (FTR). The second approach describes the Extended version of Recursive Least Square (EFRLS), where E.F. refers to the Extended Forgetting factor. Also, the computational viability of these methods was analyzed for real-time application in aerodynamic parameter estimation for both linear and non-linear systems. While the first method utilizes the frequency domain to evaluate aerodynamic parameters, the second method works when noise covariances are unknown. The performance of both methods was assessed by benchmarking against parameter estimates from established methods like Extended Kalman Filter (EKF), Unscented Kalman Filter (UNKF), and Output Error Method (OEM).

Separable Recursive Gradient Algorithm for Dynamical Systems Based on the Impulse Response Signals

The identification for process control systems is considered in this paper based on the impulse response signals from the discrete measurements. By taking advantage of impulse signals and through the model parameter decomposition, two dependent identification models are constructed and two identification sub-algorithms are presented based on the nonlinear gradient optimization. In terms of the associated items of the parameters to be estimated between two derived sub-algorithms, a separable recursive gradient parameter estimation method is proposed by designing an interactive and recursive estimation. The performance tests and the comparison experiments are carried out by the simulation examples.

Recursive parameter estimation algorithm of the Dirichlet hidden Markov model

ABSTRACTThe recursive (online, incremental) estimation of the hidden Markov model (HMM) parameters has become a more popular research subject. The complexity of the recursive methods is linear, and this complexity allows the estimation of parameters in real time. Most of the recursive parameter estimation methods use Gaussian mixtures and do not explore other distributions. However, the underlying structure of the data might be non-Gaussian. Thus, we propose a novel recursive method for estimating the parameters of the Dirichlet HMM. The Dirichlet distribution is popular because of its flexibility in modelling data. The proposed estimation is based on the maximum likelihood method, which is known to give close to optimal results. The performance of our algorithm is tested using a computer simulation and the clustering of several data-sets. Several experiments were conducted in order to compare the performance of the Gaussian HMM and Dirichlet HMM in the classification of several data-sets.

Classification of Data Stream in Sensor Network With Small Samples

Compared with conventional narrowband radar, ultra-wideband (UWB) radar has strong anti-interference performance, low-frequency, and wide-frequency characteristics, a good penetrating ability, a high-resolution range, and a good target-recognition ability. It is effective for the detection of weak signals such as breathing or motion of the human body. Therefore, a UWB radar is widely used in the field of human body target detection for earthquake and snow disasters. At present, through-wall human target detection technology using a UWB radar has two challenging problems. First, UWB radar data has a dynamic acquisition process, whereas existing detection technologies mostly employ static learning models, resulting in an inability to process and learn data features online. There is a need to address target recognition based on sensor-network data stream. Second, UWB radar faces the problem of unbalanced data classification in the identification of through-wall targets, i.e., target recognition under small-sample conditions. To address these issues, this paper proposes an adaptive incremental recursive least-squares regression parameter estimation method based on an adaptive variable sliding window, which performs Gaussian function fitting on the data streams and adapts to the mean square error and self-adaptation variable sliding window threshold comparison to adaptively block dynamic data streams. The tensor space theory is used to extract and fuse the multisensor data, and the tensor depth learning algorithm is used to improve the recognition accuracy of the target detection under small-sample conditions. To evaluate the feasibility of the proposed algorithm, we use three UWB radars to build a multistate recognition system for human targets. The data stream adaptive block effect, single and multisensor classification effects were tested under small-sample conditions. The experimental results indicate that the proposed algorithm not only accurately segmented the dynamic data streams but also effectively realized multisensor information fusion and improved the real-time target monitoring under small-sample conditions.

Fitting the exponential autoregressive model through recursive search

This paper focuses on the recursive parameter estimation methods for the exponential autoregressive (ExpAR) model. Applying the negative gradient search and introducing a forgetting factor, a stochastic gradient and a forgetting factor stochastic gradient algorithms are presented. In order to improve the parameter estimation accuracy and the convergence rate, the multi-innovation identification theory is employed to derive a forgetting factor multi-innovation stochastic gradient algorithm. A simulation example is provided to test the effectiveness of the proposed algorithms.

Upper-Limb Tele-Rehabilitation System with Force Sensorless Dynamic Gravity Compensation

Tele-rehabilitation provides remote physiotherapy services for patients who have limited access to hospitals. This paper proposes a sensorless tele-rehabilitation system for the upper-limb using two robots in master–slave configuration. The system provides a transparent haptic feeling between the therapist and the patient by simultaneous tracking of both position and torque. The torque is measured using the reaction torque observer. Furthermore, an online recursive numerical parameter estimation method is proposed to identify the gravity disturbance in bilateral teleoperation. The system automatically estimates the parameters using the reaction torque observer output’s data while the therapist is delivering remote physiotherapy services. The estimated gravity torque is compensated in the system as an improvement of the transparency of the teleoperated system. Therefore the therapist would feel only the abnormalities of the patient’s arm. Estimated parameters automatically update the system and enhance the performance. The proposed method was practically verified with a master slave tele-rehabilitation system. Results suggest the applicability of the proposed method.

Leakage detection for hydraulic IGV system in gas turbine compressor with recursive ridge regression estimation

The failure of the hydraulic Inlet guide vane (IGV) system needs to be avoided in the gas turbine compressor, since the IGV system is critical for the function and efficiency of the gas turbine and its fault can even cause the gas turbine to jump off the power grid. This paper investigates the detection of external and internal leakages, whose levels can be represented through corresponding leakage coefficients, at the cylinder in the hydraulic IGV system. Based on the dynamic model, we propose the recursive ridge regression parameter estimation method to detect and isolate different leakage coefficients under varying load. The developed algorithm is verified through experiments in a hydraulic IGV emulator. Based on experimental results, the proposed scheme can estimate leakage coefficients with good performance.

Online Monitoring of Electromagnetic Losses in an Electric Motor Indirectly Through Temperature Measurement

The condition monitoring of an electric motor is critical to its stable and reliable operation. The consequence of a fault is the variation in output performance and changes in the input electrical signature. One of the most common methods of fault detection is by analyzing the input current signature but this often requires expensive sensors. The other symptom of a faulty machine is when it runs “hot” due to an increase in losses generated. Temperature changes could be a useful indicator of the underlying fault. In this paper, a method of condition monitoring using temperature sensors embedded in an electric motor is presented. The components of electromagnetic losses generated are determined indirectly from temperature measurement in real time for a continuous drive cycle simulating normal and faulty operations. This is achieved through the inversion of the thermal model of the machine coupled with the application of a recursive parameter estimation method. Using temperature measurement for condition monitoring is advantageous since temperature sensors are low cost and already embedded in the machine for thermal protection. However, application of the method to a faulty motor and evaluation of its effectiveness in fault detection will be reported in a future work.

Recursive parameter estimation of thermostatically controlled loads via unscented Kalman filter

Abstract For thermostatically controlled loads (TCLs) to perform demand response services in real-time markets, online methods for parameter estimation are needed. As the physical characteristics of a TCL change (e.g. the contents of a refrigerator or the occupancy of a conditioned room), it is necessary to update the parameters of the TCL model. Otherwise, the TCL will be incapable of accurately predicting its potential energy demand, thereby decreasing the reliability of a TCL aggregation to perform demand response. In this paper, we investigate the potential of various unscented Kalman filter (UKF) algorithm variations to recursively identify a TCL model that is non-linear in the parameters. Experimental results demonstrate the parameter estimation of two residential refrigerators. Finally, simulation results demonstrate the incorporation of the recursive parameter estimation methods into a model predictive controller for demand response.

Heart rate regulation during cycle-ergometer exercise using damped parameter estimation method.

This paper is devoted to the problem of heart rate regulation using a model-based control strategy and a realtime damped parameter estimation scheme. The controller is a time-varying integral sliding mode controller. A recursive damped parameter estimation method is also developed, by incorporation of a weighting upon the one-step parameter variation, which in contrast to the conventional parameter estimation schemes (e.g. recursive least squares (RLS) method) can avoid the occurrence of the so-called blowup phenomena. The calculated control signals are transmitted to the subjects employing a synchronized biofeedback mechanism. The proposed control and estimation scheme were experimentally verified using twelve healthy male subjects and the results demonstrated that the designed scheme is able to regulate the HR of the exercising subjects to a predetermined HR profile preventing overshooting in the HR responses.

Model Predictive Control of Filament Tension in Textile Winding Process

Abstract. Yarn tension controlling at heart is tuning servo-motor speed on a restricted range. In this paper, we proposed an advanced model predictive control strategy to solving filament winding system time-delay problem. The application of controlled auto-regressive integrated moving-average (CARIMA) model was described the dynamic time-varying character. The parameters of CARIMA model were solved by recursive least squares parameter estimation method through input-output data. And using the receding optimization method acquire controlling amount in the future. The result of simulation shows that the method is effective and the control structure is simple.

Application of generalized predictive control to baker's yeast production

Generalized Predictive Control (GPC) was applied in the production of baker's yeast. The bioreactor was modeled with the autoregressive integrated moving average exogenous (ARIMAX) parametric difference equation model.A 2 L bioreactor with a cooling jacket was used for collecting input-output data. In order to measure pH, temperature, and dissolved oxygen in the bioreactor growth medium, suitable sensors were placed in the bioreactor. Medium temperature and the heat of the immersed heater were selected as output and manipulated variable, respectively. Square wave and a pseudo-random binary sequence (PRBS) signal were used as disturbance. Model parameters were calculated by using the recursive least square parameter estimation method. Bioreactor temperature was controlled theoretically using the GPC algorithm. The control performance was investigated by giving positive and negative step responses to the set point. The GPC algorithm holds the bioreactor temperature succesfully at the optimal set point. Optimum values of the maximum costing horizon ( N 2 ), control horizon ( N U ), and control weighting ( u ) were found to be 10, 1, and 0.005, respectively.

Evolutionary operation and control of chromatographic processes

AbstractA novel generalized run‐to‐run control (GR2R) control strategy is presented for the optimization and control of nonlinear preparative chromatographic processes. The GR2R approach synergistically employs a hybrid (both physical and empirical) model to control chromatographic processes in the presence of sporadic and autocorrelated disturbances. First, parameters of the physical model through experiments are determined, and then the physical model is used to estimate initial parameters of the nonlinear empirical model (Hammerstein) using orthogonal forward regression. Parameters of the nonlinear empirical model are updated at the end of each run using a nonlinear recursive parameter estimation method. The updated empirical model is then used in the control algorithm (model predictive control) to estimate operating conditions for the next batch. Processes operating under fixed optimal conditions are compared with those operating with GR2R control for both gradient and displacement chromatography. The GR2R outperforms the fixed conditions in the presence of various disturbances (such as bed capacity, column efficiency, and feed load) and is an effective strategy for the optimization and control of complex chromatographic processes.

Auto-SOM: recursive parameter estimation for guidance of self-organizing feature maps.

An important technique for exploratory data analysis is to form a mapping from the high-dimensional data space to a low-dimensional representation space such that neighborhoods are preserved. A popular method for achieving this is Kohonen's self-organizing map (SOM) algorithm. However, in its original form, this requires the user to choose the values of several parameters heuristically to achieve good performance. Here we present the Auto-SOM, an algorithm that estimates the learning parameters during the training of SOMs automatically. The application of Auto-SOM provides the facility to avoid neighborhood violations up to a user-defined degree in either mapping direction. Auto-SOM consists of a Kalman filter implementation of the SOM coupled with a recursive parameter estimation method. The Kalman filter trains the neurons' weights with estimated learning coefficients so as to minimize the variance of the estimation error. The recursive parameter estimation method estimates the width of the neighborhood function by minimizing the prediction error variance of the Kalman filter. In addition, the "topographic function" is incorporated to measure neighborhood violations and prevent the map's converging to configurations with neighborhood violations. It is demonstrated that neighborhoods can be preserved in both mapping directions as desired for dimension-reducing applications. The development of neighborhood-preserving maps and their convergence behavior is demonstrated by three examples accounting for the basic applications of self-organizing feature maps.

FIT - Filtering and Identification Tool

The program "Filtering and Identification Tool" designed for MATLAB provides an easy to handle tool for linear system identification of continuous time domain systems. But also discrete time models may be identified. The only property the process model must fulfill is that it has to be linear in the parameters. A graphical user interface guides the research engineer through all steps. As most of the time consuming algorithms are implemented as C-functions, the identification even with a huge amount of data takes only few seconds. To identify continuous time process models, derivatives of the input and output signals are required. However, these signals often cannot be measured. Therefore digital filters such as state variable filter (SVF) and differentiating finite impulse response (FIR) filters are integrated into FIT to provide the necessary derivatives. For the identification task various recursive parameter estimation methods like recursive least means squares (RLS), discrete square root filter in information form (DSFI), normalized least means squares (NLMS), etc. are included, too. Recursive algorithms with exponential fading memory (variable step size in case of NLMS) were chosen in order to identify time variant systems. But also for the offline design of real-time fault detection or adaptive control schemes using parameter estimation methods a variable forgetting factor is important to be able to track varying parameters. Thus, the main advantage of the Filtering and Identification Tool in comparison to existing software tools for system identification is the integration of both parameter estimation methods and differentiating filters.

Recursive parameter estimation methods: An adaptive filtering perspective

This tutorial provides an overview of recursive parameter estimation methods from the viewpoint of the adaptive filtering field. Specific topics to be discussed include gradient versus least-squares techniques, adaptive infinite-impulse response filters, and bias removal methods. Particular emphasis is placed on the analytical behaviors of the algorithms, their estimation characteristics, and their tracking abilities in mildly nonstationary environments. Applications of the methods to identification problems in acoustics are discussed. [This work has been supported by NSF Grant No. MIP-9501680.]

Block algorithms for the parametric estimation of signals and systems

Existing recursive parameter estimation methods use approximated covariance and gradient matrices which are actually computed as functions of the present parameter vector thetaŝ(t) by the matrices computed as functions of all previous parameter estimates thetaŝ(i) for i ≤ t. By reducing the approximations considerably, modified versions of the recursive identification algorithms are obtained. Considering the local averages of the covariance and the gradient and clubbing conveniently with the block nature of estimators, efficient block versions of these algorithms are obtained.

DISP - A Program Package for Digital Control System Education

DISP is a program package for analysis and transformation of discrete systems, for identification with recursive parameter estimation methods and for simulation of difference equations. The programs support the education of theory and problems of the lecture Digital Control Systems for undergraduate students of automatic control at the Ruhr-University of Bochum. DISP is written as an educational software with special handling features for students. It is built up in chapters and pages, which can be read forward and backward correspondend to a book. Menue technique, softkey control, error messages and default values guarantee a simple use without a manual.

Identification of Nonlinear Vibrating Structures: Part I—Formulation

A self-starting multistage, time-domain procedure is presented for the identification of nonlinear, multi-degree-of-freedom systems undergoing free oscillations or subjected to arbitrary direct force excitations and/or nonuniform support motions. Recursive least-squares parameter estimation methods combined with non-parametric identification techniques are used to represent, with sufficient accuracy, the identified system in a form that allows the convenient prediction of its transient response under excitations that differ from the test signals. The utility of this procedure is demonstrated in a companion paper.