scholarly journals Real-Time Identification of Dynamic Loads Using Inverse Solution and Kalman Filter

2020 ◽  
Vol 10 (19) ◽  
pp. 6767
Author(s):  
Jinhui Jiang ◽  
Shuyi Luo ◽  
M. Shadi Mohamed ◽  
Zhongzai Liang
Keyword(s):  
Kalman Filter ◽  
Real Time ◽  
Earthquake Engineering ◽  
State Vector ◽  
The State ◽  
Dynamic Loads ◽  
Unbiased Estimation ◽  
System Response ◽  
Structural Dynamic ◽  
Online Identification

Evaluating dynamic loads in real time is crucial for health monitoring, fault diagnosis and fatigue analysis in aerospace, automotive and earthquake engineering among other vibration related applications. Developing such algorithms can be vital for several safety and performance functionalities. Therefore, over the past few years the identification of dynamic loads has attracted a lot of attention; however, little literature on the online identification can be found. In this paper, we propose an online-identification method of structural dynamic loads so that the dynamic load is evaluated in real time and while the system response is still being measured. This is achieved by significantly improving the identification efficiency while retaining a high accuracy. The proposed method which is based on Kalman filter, is introduced in detail for a finite as well as an infinite number of degrees of freedom. Starting from an initial guess of the state vector we evaluate the error covariance, which then helps to identify the value of the excitation force using a weighted least square method and minimizing the covariance unbiased estimation. This is repeated at certain time intervals i.e., time steps where the state vector is updated in real time as acceleration measurements are updated. The feasibility of the method is validated using numerical simulations and an experimental verification where a detailed LabVIEW (National Instruments Ltd.) implementation is provided.

scholarly journals A Strong Tracking Mixed-Degree Cubature Kalman Filter Method and Its Application in a Quadruped Robot

Sensors ◽  
2020 ◽  
Vol 20 (8) ◽  
pp. 2251 ◽  
Author(s):  
Jikai Liu ◽  
Pengfei Wang ◽  
Fusheng Zha ◽  
Wei Guo ◽  
Zhenyu Jiang ◽  
...  
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Real Time ◽  
Quadruped Robot ◽  
The State ◽  
Estimation Accuracy ◽  
Robot System ◽  
Calculation Time ◽  
Motion State ◽  
Cubature Kalman Filter

The motion state of a quadruped robot in operation changes constantly. Due to the drift caused by the accumulative error, the function of the inertial measurement unit (IMU) will be limited. Even though multi-sensor fusion technology is adopted, the quadruped robot will lose its ability to respond to state changes after a while because the gain tends to be constant. To solve this problem, this paper proposes a strong tracking mixed-degree cubature Kalman filter (STMCKF) method. According to system characteristics of the quadruped robot, this method makes fusion estimation of forward kinematics and IMU track. The combination mode of traditional strong tracking cubature Kalman filter (TSTCKF) and strong tracking is improved through demonstration. A new method for calculating fading factor matrix is proposed, which reduces sampling times from three to one, saving significantly calculation time. At the same time, the state estimation accuracy is improved from the third-degree accuracy of Taylor series expansion to fifth-degree accuracy. The proposed algorithm can automatically switch the working mode according to real-time supervision of the motion state and greatly improve the state estimation performance of quadruped robot system, exhibiting strong robustness and excellent real-time performance. Finally, a comparative study of STMCKF and the extended Kalman filter (EKF) that is commonly used in quadruped robot system is carried out. Results show that the method of STMCKF has high estimation accuracy and reliable ability to cope with sudden changes, without significantly increasing the calculation time, indicating the correctness of the algorithm and its great application value in quadruped robot system.

An Advanced Formulation of Kalman Filter Time Series Reference Frame Realization for Geophysical Applications

2020 ◽  
Author(s):  
Xiaoping Wu ◽  
Bruce Haines ◽  
Michael Heflin ◽  
Felix Landerer
Keyword(s):  
Time Series ◽  
Kalman Filter ◽  
Reference Frame ◽  
State Vector ◽  
Terrestrial Reference Frame ◽  
Covariance Matrices ◽  
Time Variable ◽  
The State ◽  
Geocenter Motion ◽  
Over Time

<p>A Kalman filter and time series approach to the International Terrestrial Reference Frame (ITRF) realization (KALREF) has been developed and used in JPL. KALREF combines weekly or daily SLR, VLBI, GNSS and DORIS data and realizes a terrestrial reference frame in the form of time-variable geocentric station coordinate time series. The origin is defined at nearly instantaneous Center-of-Mass of the Earth system (CM) sensed by weekly SLR data and the scale is implicitly defined by the weighted averages of those of weekly SLR and daily VLBI data. The standard KALREF formulation describes the state vector in terms of time variable station coordinates and other constant parameters. Such a formulation is fine for station positions and their uncertainties or covariance matrices at individual epochs. However, coordinate errors are strongly correlated over time given KALREF’s unique nature of combining different technique data with various frame strengths through local tie measurements and co-motion constraints and its use of random walk processes. For long time series and large space geodetic networks in the ITRF, KALREF cannot keep track of such correlations over time. If they are ignored when forming geocentric displacements for geophysical inverse or network shift geocenter motion studies, the covariance matrices of coordinate differences cannot adequately represent those of displacements. Consequently, significant non-uniqueness and inaccuracies would occur in the results of studies using such matrices. To overcome this difficulty, an advanced KALREF formulation is implemented that features explicit displacement parameters in the state vector that would allow the Kalman filter and smoother to compute and return covariance matrices of displacements. The use of displacement covariance matrices reduces the impact of time correlated errors and completely solves the non-uniqueness problem. However, errors in the displacements are still correlated in time. Further calibrations are needed to accurately assess covariance matrices of derivative quantities such as averages, velocities and accelerations during various time periods. We will present KALREF results of the new formulation and their use along with newly reprocessed RL06 GRACE gravity data in a new unified inversion for geocenter motion.</p>

scholarly journals Structural Stiffness Identification Based on the Extended Kalman Filter Research

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Fenggang Wang ◽  
Xianzhang Ling ◽  
Xun Xu ◽  
Feng Zhang
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
State Equation ◽  
The State ◽  
Physical Parameters ◽  
Structural Stiffness ◽  
Structural Dynamic ◽  
Discrete State ◽  
Response Acquisition ◽  
Shear Structure

For the response acquisition of the structure section measuring points, the method of identifying the structural stiffness parameters is developed by using the extended Kalman filter. The state equation of structural system parameter is a nonlinear equation. Dispersing the structural dynamic equation by using Newmark-βmethod, the state transition matrix of discrete state equation is deduced and the solution of discrete state equation is simplified. The numerical simulation shows that the error of structural recognition doesnot exceed 5% when the noise level is 3%. It meets the requirements of the error limit of the engineering structure, which indicates that the derivation described in this paper has the robustness for the structural stiffness recognition. Shear structure parameter identification examples illustrate its applicability, and the method can also be used to identify physical parameters of large structure.

Identification of Stochastic System and Controller via Projection Filters

1996 ◽  
Vol 118 (2) ◽  
pp. 169-176 ◽  
Author(s):  
Hyun Chang Lee ◽  
Min-Hung Hsiao ◽  
Jen-Kuang Huang ◽  
Chung-Wen Chen
Keyword(s):  
Kalman Filter ◽  
State Space ◽  
Stochastic System ◽  
State Space Model ◽  
Open Loop ◽  
The State ◽  
Loop System ◽  
Test Facility ◽  
System Response ◽  
Space Model

A method based on projection filters is presented for identifying an open-loop stochastic system with an existing feedback controller. The projection filters are derived from the relationship between the state-space model and the AutoRegressive with eXogeneous input (ARX) model including the system, Kalman filter and controller. Two ARX models are identified from the control input, closed-loop system response and feedback signal using least-squares method. Markov parameters of the open-loop system, Kalman filter and controller are then calculated from the coefficients of the identified ARX models. Finally, the state-space model of the open-loop stochastic system and the gain matrices for the Kalman filter and controller are realized. The method is validated by simulations and test data from an unstable large-angle magnetic suspension test facility.

Image-based visual servoing with depth estimation

2021 ◽  
pp. 014233122110646
Author(s):  
Qingxuan Gongye ◽  
Peng Cheng ◽  
Jiuxiang Dong
Keyword(s):  
Real Time ◽  
State Vector ◽  
Visual Servoing ◽  
Jacobian Matrix ◽  
Fuzzy Controller ◽  
Image Plane ◽  
Depth Estimation ◽  
The State ◽  
Estimation Problem ◽  
Depth Information

For the depth estimation problem in the image-based visual servoing (IBVS) control, this paper proposes a new observer structure based on Kalman filter (KF) to recover the feature depth in real time. First, according to the number of states, two different mathematical models of the system are established. The first one is to extract the depth information from the Jacobian matrix as the state vector of the system. The other is to use the depth information and the coordinate point information of the two-dimensional image plane as the state vector of the system. The KF is used to estimate the unknown depth information of the system in real time. And an IBVS controller gain adjustment method for 6-degree-of-freedom (6-DOF) manipulator is obtained using fuzzy controller. This method can obtain the gain matrix by taking the depth and error information as the input of the fuzzy controller. Compared with the existing works, the proposed observer has less redundant motion while solving the Jacobian matrix depth estimation problem. At the same time, it will also be beneficial to reducing the time for the camera to reach the target. Conclusively, the experimental results of the 6-DOF robot with eye-in-hand configuration demonstrate the effectiveness and practicability of the proposed method.

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 Application of Analogue Derivators for Obtaining Direct Non-Measurable Components of the State Vector in Crane Control

2019 ◽  
Vol 69 (4) ◽  
pp. 33-44
Author(s):  
Grosinger Patrik ◽  
Šolek Peter
Keyword(s):  
Kalman Filter ◽  
State Vector ◽  
The State ◽  
Measurement Noise ◽  
Controlled System ◽  
Crane Control ◽  
Luenberger Observer ◽  
Numerical Derivative

AbstractThis paper presents a simple-to-use system for estimating non-measurable components of crane state vector considering parameter changes. To obtain them, it is possible to use a numerical derivative, where the measurement noise causes great inaccuracies, or the Luenberger observer and Kalman filter, which require knowledge of the dynamics of the controlled system, which is constantly changing with the crane.

scholarly journals Two-Step Adaptive Augmented Unscented Kalman Filter for Roll Angles of Spinning Missiles Based on Magnetometer Measurements

2018 ◽  
Vol 51 (3-4) ◽  
pp. 73-82 ◽  
Author(s):  
Xiaolong Yan ◽  
Guoguang Chen ◽  
Xiaoli Tian
Keyword(s):  
Kalman Filter ◽  
State Vector ◽  
Unscented Kalman Filter ◽  
Sampling Rate ◽  
The State ◽  
Roll Angle ◽  
Estimation Accuracy ◽  
Measurement Circuit ◽  
Kalman Filter Algorithm ◽  
Stop Rule

It is critical to measure the roll angle of a spinning missile quickly and accurately. Magnetometers are commonly used to implement these measurements. At present, the estimation of roll angle parameters is usually performed with the unscented Kalman filter algorithm. In this paper, the two-step adaptive augmented unscented Kalman filter algorithm is proposed to calibrate the biaxial magnetometer and circuit measurements quickly, which allows accurate estimates of the missile roll angle. Unlike the existing algorithms, the state vector of the algorithm is based on the missile roll angle parameters and the error factors caused by the magnetometer and the measurement circuit errors. Next, a two-step fast fitting algorithm is used to fit the initial value. After satisfying the stop rule, the state vector of the filter is configured to estimate the roll angle parameters and the calibration parameters. This method is evaluated by running numerous simulations. In the experiment, the algorithm completes the calibration of the magnetometer and the measurement circuit 1 s after the missile launches, with a sampling rate of 1 ms and an output roll attitude angle with a 0.0015 rad precision. The conventional unscented Kalman filter algorithm requires more time to achieve such a high accuracy. The simulation results demonstrate that the proposed two-step augmented unscented Kalman filter outperforms the conventional unscented Kalman filter in its estimation accuracy and convergence characteristics.

A Kalman Filter Framework for High-Dimensional Sensor Fusion Using Stochastic Non-Linear Networks

2014 ◽  
Author(s):  
George M. Lloyd
Keyword(s):  
Kalman Filter ◽  
Process Model ◽  
State Space Model ◽  
Dimensional Subspace ◽  
The State ◽  
Sensor Data ◽  
System Response ◽  
Linear Networks ◽  
Non Linear ◽  
Low Dimensional

The textbook Kalman Filter (LKF) seeks to estimate the state of a linear system based on having two things in hand: a.) a reasonable state-space model of the underlying process and its noise components; b.) imperfect (noisy) measurements obtained from the process via one or more sensors. The LKF approach results in a predictor-corrector algorithm which can be applied recursively to correct predictions from the state model so as to yield posterior estimates of the current process state, as new sensor data are made available. The LKF can be shown to be optimal in a Gaussian setting and is eminently useful in practical settings when the models and measurements are stochastic and non-stationary. Numerous extensions of the KF filter have been proposed for the non-linear problem, such as extended Kalman Filters (EKF) and ‘ensemble’ filters (EnKF). Proofs of optimality are difficult to obtain but for many problems where the ‘physics’ is of modest complexity EKF’s yield algorithms which function well in a practical sense; the EnKF also shows promise but is limited by the requirement for sampling the random processes. In multi-physics systems, for example, several complications arise, even beyond non-Gaussianity. On the one hand, multi-physics effects may include multi-scale responses and path dependency, which may be poorly sampled by a sensor suite (tending to favor low gains). One the other hand, as more multi-physics effects are incorporated into a model, the model itself becomes a less and less perfect model of reality (tending to favor high gains). For reasons such as these suitable estimates of the joint system response are difficult to obtain, as are corresponding joint estimates of the sensor ensemble. This paper will address these issues in a two-fold way — first by a generalized process model representation based on regularized stochastic non-linear networks (Snn), and second by transformation of the process itself by an adaptive low-dimensional subspace in which the update step on the residual can be performed in a space commensurate with the available information content of the process and measured response.

Sign in / Sign up

Export Citation Format

Share Document