Measurement of Step Responses of Flowrate in a Pipe Using a Kalman-Filtering Laminar Flowmeter

2021 ◽  
Author(s):  
Kazushi Sanada
Keyword(s):  
Kalman Filter ◽  
Laminar Flow ◽  
Response Time ◽  
Kalman Filtering ◽  
The State ◽  
Step Response ◽  
Working Fluid ◽  
State Variables ◽  
Turbulent Friction ◽  
Experimental Calibration

Abstract The aim of our research project is to develop a Kalman filter system which estimates unsteady flowrate of a pipe using a laminar flowmeter. In this study, incompressible flow is assumed as working fluid. When the flow becomes turbulent, it is difficult to establish flow model for turbulent friction. In this study, a laminar flowmeter is constructed in which thirty-two narrow pipes of 1mm in inner diameter are bundled and inserted in main flow path. When fluid flow in the narrow pipe is laminar flow, the Kalman filter theory can be applied to the flow of the narrow pipe. Kalman filter is applied to one of narrow pipes of laminar flowmeter. Both upstream and downstream pressure signals of the targeted narrow pipe are input to the Kalman filter. Midpoint pressure measured by a pressure sensor is compared with midpoint pressure signal which is estimated by the Kalman filter. When flow is laminar flow or the system has linear characteristics, an error signal between estimated pressure and measured pressure decreases according to Kalman filter principle. As a result, because the state variables of the Kalman filter converge to real variables, unsteady flowrate is estimated from the state variables of the Kalman filter. Experimental calibration of the Kalman-filtering laminar flowmeter under steady-state flow condition has been performed. In this study, experiments of step response of flowrate in a pipe are conducted by constructing an experimental circuit using solenoid valves. The purpose of experiment is confirmation of a response time of the Kalman-filtering laminar flowmeter. As a result of experiments, it was shown that the response time is 0.05s.

Dynamic Reservoir Data Assimilation With an Efficient, Dimension-Reduced Kalman Filter

SPE Journal ◽  
2007 ◽  
Vol 12 (01) ◽  
pp. 108-117 ◽  
Author(s):  
Dongxiao Zhang ◽  
Zhiming Lu ◽  
Yan Chen
Keyword(s):  
Kalman Filter ◽  
Covariance Matrix ◽  
Kalman Filtering ◽  
Large Scale ◽  
The State ◽  
State Variables ◽  
Reservoir Properties ◽  
Heterogeneous Reservoirs ◽  
Variable Permeability ◽  
Direct Observations

Summary Kalman filter-based methods have been widely applied for assimilating new measurements to continuously update the estimate of state variables, such as reservoir properties and responses. The standard Kalman filtering scheme requires computing and storing the covariance matrix of state variables, which is computationally expensive for large-scale problems with millions of gridblocks. In the ensemble Kalman filter (EnKF), this problem is alleviated with sampling from a limited number of realizations and computing the required subset of the covariance matrix at each update. However, the goodness of the (ensemble) covariance approximated from the limited ensemble depends on the number of realizations used and the representativity of a given ensemble. In this study, we propose an efficient, dimension-reduced Kalman filtering scheme based on Karhunen-Loeve (KL) and other orthogonal polynomial decompositions of the state variables. We consider flow in heterogeneous reservoirs with spatially variable permeability. The reservoir responses such as pressure are measured at some locations at various time intervals. The aim is to dynamically characterize the reservoir properties and to predict the reservoir performance and its uncertainty at future times. In our scheme, the covariance of the reservoir properties is approximated by a small set of eigenvalues and eigenfunctions using the KL decomposition and the reconstruction of the covariance from the KL decomposition can be done whenever needed. In each update, the forecast step is solved using the KL-based moment method, giving a set of functions from which the mean and covariance of the state variables can be constructed, when needed. The statistics of both the reservoir properties and the reservoir responses are then updated with the available measurements at this time using the auto- and cross-covariances obtained from the forecast step. The new approach is illustrated on a heterogeneous reservoir with dynamic measurements and the results are compared with those from the EnKF method, in terms of accuracy and efficiency. Introduction Owing to the high cost associated with direct measurements of reservoir properties, for instance permeability and porosity, the number of direct observations is always limited. However, the reservoir exhibits a high degree of spatial variability at all length scales resulted from its intrinsically complicated nature. This combination of significant spatial heterogeneity with a relatively small number of direct observations leads to uncertainty in characterizing reservoir properties, which in turn results in uncertainty in estimating or predicting the corresponding reservoir responses.

scholarly journals Kalman Filtering Applied to Induction Motor State Estimation

2020 ◽  
Author(s):  
Yassine Zahraoui ◽  
Mohamed Akherraz
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Induction Motor ◽  
Kalman Filtering ◽  
Speed Estimation ◽  
Stochastic Algorithm ◽  
State Variables ◽  
Extended Kalman Filtering ◽  
Filtering Theory ◽  
State Observation

This chapter presents a full definition and explanation of Kalman filtering theory, precisely the filter stochastic algorithm. After the definition, a concrete example of application is explained. The simulated example concerns an extended Kalman filter applied to machine state and speed estimation. A full observation of an induction motor state variables and mechanical speed will be presented and discussed in details. A comparison between extended Kalman filtering and adaptive Luenberger state observation will be highlighted and discussed in detail with many figures. In conclusion, the chapter is ended by listing the Kalman filtering main advantages and recent advances in the scientific literature.

scholarly journals Noise control with Kalman filter for active headrest

2021 ◽  
Vol 39 (5) ◽  
pp. 937-944
Author(s):  
Lei WANG ◽  
Kean CHEN ◽  
Jian XU ◽  
Wang QI
Keyword(s):  
Kalman Filter ◽  
Noise Control ◽  
Active Noise Control ◽  
Noise Signal ◽  
State Equation ◽  
The State ◽  
Convergence Speed ◽  
State Variables ◽  
Gradient Based ◽  
Convergence Performance

A control strategy with Kalman filter (KF) is proposed for active noise control of virtual error signal for active headset. Comparing with the gradient based algorithm, KF algorithm has faster convergence speed and better convergence performance. In this paper, the state equation of the system is established on the basis of virtual error sensing, and only the weight coefficients of the control filter are considered in the state variables. In order to ensure the convergence performance of the algorithm, an online updating strategy of KF parameters is proposed. The fast-array method is also introduced into the algorithm to reduce the computation. The simulation results show that the present strategy can improve the convergence speed and effectively reduce the noise signal at the virtual error point.

Design of Extended Kalman Filter for a Shape Memory Alloy Manipulator

2003 ◽  
Author(s):  
Mohammad H. Elahinia ◽  
Hashem Ashrafiuon ◽  
Mehdi Ahmadian ◽  
William T. Baumann
Keyword(s):  
Kalman Filter ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Extended Kalman Filter ◽  
State Space Model ◽  
Angular Position ◽  
The State ◽  
State Variables ◽  
Time Step ◽  
Noisy Measurements

This paper presents an Extended Kalman Filter (EKF) for estimation of the state variables of a single degree of freedom rotary manipulator actuated by Shape Memory Alloy (SMA). A state space model for the SMA manipulator is presented. The model includes nonlinear dynamics of the manipulator, constitutive model of Shape Memory Alloy, and the electrical and heat transfer behavior of SMA wire. In the experimental setup, angular position of the arm is the only state variable that is measured. The other state variables of the system are arm’s angular velocity, SMA wire’s stress, temperature and the Martensite factor, which are not available experimentally due to measurement difficulties. Hence, a model-based state estimator that works with noisy measurements is presented based on the Extended Kalman Filter. This estimator predicts the state vector at each time step and corrects its prediction based on the angular position of the arm which can be measured experimentally. The state variables collected through model simulations are also used to evaluate the performance of the EKF. Several EKF simulations are presented that show accurate, and robust performance of the estimator for different types of inputs.

Parallel Optimal Kalman Filtering for Stochastic Systems in Multimodeling Form

1999 ◽  
Vol 122 (3) ◽  
pp. 542-550 ◽  
Author(s):  
Cyril Coumarbatch ◽  
Zoran Gajic
Keyword(s):  
Kalman Filter ◽  
Kalman Filtering ◽  
Kalman Filters ◽  
Stochastic Systems ◽  
State Variables ◽  
State Transformation ◽  
Eighth Order ◽  
Reduced Order ◽  
Filtering Technique ◽  
Ill Conditioning

In this paper we show how to completely and exactly decompose the optimal Kalman filter of stochastic systems in multimodeling form in terms of one pure-slow and two pure-fast, reduced-order, independent, Kalman filters. The reduced-order Kalman filters are all driven by the system measurements. This leads to a parallel Kalman filtering scheme and removes ill-conditioning of the original full-order singularly perturbed Kalman filter. The results obtained are valid for steady state. In that direction, the corresponding algebraic filter Riccati equation is completely decoupled and solved in terms of one pure-slow and two pure fast, reduced-order, independent, algebraic Riccati equations. A nonsingular state transformation that exactly relates the state variables in the original and new coordinates (in which the required decomposition is achieved) is also established. The eighth order model of a passenger car under road disturbances is used to demonstrate efficiency of the proposed filtering technique. [S0022-0434(00)01703-2]

Application of the Extended Kalman Filter to Control of a Shape Memory Alloy Arm

2003 ◽  
Author(s):  
Mohammad H. Elahinia ◽  
Hashem Ashrafiuon ◽  
Mehdi Ahmadian ◽  
Daniel J. Inman
Keyword(s):  
Kalman Filter ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Extended Kalman Filter ◽  
State Vector ◽  
Angular Position ◽  
The State ◽  
State Variables ◽  
Time Step ◽  
State Variable

This paper presents a robust nonlinear control that uses a state variable estimator for control of a single degree of freedom rotary manipulator actuated by Shape Memory Alloy (SMA) wire. A model for SMA actuated manipulator is presented. The model includes nonlinear dynamics of the manipulator, a constitutive model of the Shape Memory Alloy, and the electrical and heat transfer behavior of SMA wire. The current experimental setup allows for the measurement of only one state variable which is the angular position of the arm. Due to measurement difficulties, the other three state variables, arm angular velocity and SMA wire stress and temperature, cannot be directly measured. A model-based state estimator that works with noisy measurements is presented based on the Extended Kalman Filter (EKF). This estimator predicts the state vector at each time step and corrects its prediction based on the angular position measurements. The estimator is then used in a nonlinear and robust control algorithm based on Variable Structure Control (VSC). The VSC algorithm is a control gain switching technique based on the arm angular position (and velocity) feedback and EKF estimated SMA wire stress and temperature. The state vector estimates help reduce or avoid the undesirable and inefficient overshoot problem in SMA one-way actuation control.

scholarly journals Simultaneous estimation of model state variables and observation and forecast biases using a two-stage hybrid Kalman filter

2013 ◽  
Vol 10 (4) ◽  
pp. 5169-5224 ◽  
Author(s):  
V. R. N. Pauwels ◽  
G. J. M. De Lannoy ◽  
H.-J. Hendricks Franssen ◽  
H. Vereecken
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
The State ◽  
Bias Error ◽  
Simultaneous Estimation ◽  
State Variables ◽  
Two Stage ◽  
Forecast Bias ◽  
Error Covariance ◽  
Observation Bias

Abstract. In this paper, we present a two-stage hybrid Kalman filter to estimate both observation and forecast bias in hydrologic models, in addition to state variables. The biases are estimated using the Discrete Kalman Filter, and the state variables using the Ensemble Kalman Filter. A key issue in this multi-component assimilation scheme is the exact partitioning of the difference between observation and forecasts into state, forecast bias and observation bias updates. Here, the error covariances of the forecast bias and the unbiased states are calculated as constant fractions of the biased state error covariance, and the observation bias error covariance is a function of the observation prediction error covariance. In a series of synthetic experiments, focusing on the assimilation of discharge into a rainfall-runoff model, it is shown that both static and dynamic observation and forecast biases can be successfully estimated. The results indicate a strong improvement in the estimation of the state variables and resulting discharge as opposed to the use of a bias-unaware Ensemble Kalman Filter. The results suggest that a better performance of data assimilation methods should be possible if both forecast and observation biases are taken into account.

scholarly journals The Extended Kalman Filter in the Dynamic State Estimation of Electrical Power Systems

Enfoque UTE ◽  
2018 ◽  
Vol 9 (4) ◽  
pp. 120-130
Author(s):  
Holger Ignacio Cevallos Ulloa ◽  
Gabriel Intriago ◽  
Douglas Plaza ◽  
Roger Idrovo
Keyword(s):  
Kalman Filter ◽  
Power Systems ◽  
State Estimation ◽  
Extended Kalman Filter ◽  
Electrical Power ◽  
The State ◽  
Dynamic State ◽  
State Variables ◽  
Electrical Power Systems ◽  
Error Index

The state estimation and the analysis of load flow are very important subjects in the analysis and management of Electrical Power Systems (EPS). This article describes the state estimation in EPS using the Extended Kalman Filter (EKF) and the method of Holt to linearize the process model and then calculates a performance error index as indicators of its accuracy. Besides, this error index can be used as a reference for further comparison between methodologies for state estimation in EPS such as the Unscented Kalman Filter, the Ensemble Kalman Filter, Monte Carlo methods, and others. Results of error indices obtained in the simulation process agree with the order of magnitude expected and the behavior of the filter is appropriate due to follows adequately  the true value of the state variables. The simulation was done using Matlab and the electrical system used corresponds to the IEEE 14 and 30 bus test case systems. State Variables to consider in this study are the voltage and angle magnitudes.

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