scholarly journals Uncertainty Analysis and Experimental Validation of Identifying the Governing Equation of an Oscillator Using Sparse Regression

2022 ◽  
Vol 12 (2) ◽  
pp. 747
Author(s):  
Yaxiong Ren ◽  
Christian Adams ◽  
Tobias Melz

In recent years, the rapid growth of computing technology has enabled identifying mathematical models for vibration systems using measurement data instead of domain knowledge. Within this category, the method Sparse Identification of Nonlinear Dynamical Systems (SINDy) shows potential for interpretable identification. Therefore, in this work, a procedure of system identification based on the SINDy framework is developed and validated on a single-mass oscillator. To estimate the parameters in the SINDy model, two sparse regression methods are discussed. Compared with the Least Squares method with Sequential Threshold (LSST), which is the original estimation method from SINDy, the Least Squares method Post-LASSO (LSPL) shows better performance in numerical Monte Carlo Simulations (MCSs) of a single-mass oscillator in terms of sparseness, convergence, identified eigenfrequency, and coefficient of determination. Furthermore, the developed method SINDy-LSPL was successfully implemented with real measurement data of a single-mass oscillator with known theoretical parameters. The identified parameters using a sweep signal as excitation are more consistent and accurate than those identified using impulse excitation. In both cases, there exists a dependency of the identified parameter on the excitation amplitude that should be investigated in further research.

2011 ◽  
Vol 57 (No. 11) ◽  
pp. 545-554
Author(s):  
M. Malý ◽  
Z. Kroupová ◽  
D. Žídková ◽  
J. Peterová ◽  
L. Šobrová ◽  
...  

The main aim of the paper was a partial analysis of the production potential for pig fattening in the Czech Republic. This aim was achieved by econometric modelling of the production function, which was specified as a Cobb-Douglas function, with the level of average daily increase as the dependent variable, and feed compounds, mortality and weight of new stock as independent variables. The model was specified as a fixed effect model, and the parameters of the function were estimated by the method of least squares dummy variable, based on the ordinary least squares method. Verification of the estimated model was based on a t-test, coefficient of determination, Wald test, autoregressive test, and test of normality distribution of residuals. Subsequently, the estimated function was analysed and significant determinants of production were identified. The behaviour of the production functions was analysed for the average and marginal productions. The functions were also illustrated in graphs of production surfaces, from which the maps of isoproduction functions were derived. The isoproduction functions were used for the final analysis of the potential for pork production. The analysis was based on panel data from 32 farms focused on pig fattening, collected by our own survey. The research indicated significant differences between the surveyed farms. It also declared the most important factor of final production to be, with 99% probability, the new stock weight. The second most important determinant of final production is the feed compound A3, which is used in the final stage of fattening. For maximized production, the farmer should focus on the weight of pigs coming into fattening, choose the biggest one, and introduce the use of the feed compound A3. The results in the submitted paper should also be used by farmers to evaluate their production activity, and to compare their actual output with the theoretical value enumerated by the production function.


Author(s):  
G. Navratil ◽  
E. Heer ◽  
J. Hahn

Geodetic survey data are typically analysed using the assumption that measurement errors can be modelled as noise. The least squares method models noise with the normal distribution and is based on the assumption that it selects measurements with the highest probability value (Ghilani, 2010, p. 179f). There are environment situations where no clear maximum for a measurement can be detected. This can happen, for example, if surveys take place in foggy conditions causing diffusion of light signals. This presents a problem for automated systems because the standard assumption of the least squares method does not hold. A measurement system trying to return a crisp value will produce an arbitrary value that lies within the area of maximum value. However repeating the measurement is unlikely to create a value following a normal distribution, which happens if measurement errors can be modelled as noise. In this article we describe a laboratory experiment that reproduces conditions similar to a foggy situation and present measurement data gathered from this setup. Furthermore we propose methods based on fuzzy set theory to evaluate the data from our measurement.


1978 ◽  
Vol 15 (1) ◽  
pp. 145-153
Author(s):  
Berend Wierenga

The author presents a new method for estimating the parameters of the linear learning model. The procedure, essentially a least squares method, is easy to carry out and avoids certain difficulties of earlier estimation procedures. Applications to three different data sets are reported, as well as results from a goodness-of-fit test. A simulation study was carried out to validate the method. The outcomes are compared with those obtained from the minimum chi square estimation method. The results of the new method appear to be satisfactory.


2004 ◽  
Vol 127 (1) ◽  
pp. 50-56 ◽  
Author(s):  
F. Xi ◽  
D. Nancoo ◽  
G. Knopf

In this paper a method is proposed to register three-dimensional line laser scanning data acquired in two different viewpoints. The proposed method is based on three-point position measurement by scanning three reference balls to determine the transformation between two views. Since there are errors in laser scanning data and sphere fitting, the two sets of three-point position measurement data at two different views are both subject to errors. For this reason, total least-squares methods are applied to determine the transformation, because they take into consideration the errors both at inputs and outputs. Simulations and experiment are carried to compare three methods, namely, ordinary least-squares method, unconstrained total least-squares method, and constrained total least-squares method. It is found that the last method gives the most accurate results.


1994 ◽  
Vol 116 (3) ◽  
pp. 890-893 ◽  
Author(s):  
G. Zak ◽  
B. Benhabib ◽  
R. G. Fenton ◽  
I. Saban

Significant attention has been paid recently to the topic of robot calibration. To improve the robot’s accuracy, various approaches to the measurement of the robot’s position and orientation (pose) and correction of its kinematic model have been proposed. Little attention, however, has been given to the method of estimation of the kinematic parameters from the measurement data. Typically, a least-squares solution method is used to estimate the corrections to the parameters of the model. In this paper, a method of kinematic parameter estimation is proposed where a standard least-squares estimation procedure is replaced by weighted least-squares. The weighting factors are calculated based on all the a priori available statistical information about the robot and the pose-measuring system. By giving greater weight to the measurements made where the standard deviation of the noise in the data is expected to be lower, a significant reduction in the error of the kinematic parameter estimates is made possible. The improvement in the calibration results was verified using a calibration simulation algorithm.


Author(s):  
WEN-LIANG HUNG ◽  
YUAN-CHEN LIU

The purpose of this paper is to find a robust estimation method for a two-parameter Weibull distribution when outliers are present. This is a relevant problem because of the usefulness of the Weibull distribution in life testing and reliability theory. For that purpose, a cluster-wise fuzzy least-squares algorithm with a noise cluster is used. This is because a noise cluster can be used for compensating the effects of outliers. Numerical comparisons between this fuzzy least-squares algorithm and the existing methods are implemented. According to these comparisons, it is suggested that the proposed fuzzy least-squares algorithm is preferable when the sample size is large.


2021 ◽  
Vol 11 (9) ◽  
pp. 4000
Author(s):  
Namju Byun ◽  
Jeonghwa Lee ◽  
Keesei Lee ◽  
Young-Jong Kang

The structural deformed shape (SDS) is considered an important factor for evaluating structural conditions owing to its direct relationship with structural stiffness. Recently, an SDS estimation method based on displacement data from a limited number of data points was developed. Although the method showed good performance with a sufficient number of measured data points, application of the SDS estimation method for on-site structures has been quite limited because collecting sufficient displacement data measured from a Global Navigation Satellite System (GNSS) can be quite expensive. Thus, the development of an affordable SDS estimation method with a certain level of accuracy is essential for field application of the SDS estimation technique. This paper proposes an improved SDS estimation method using displacement data combined with additional slope and strain data that can improve the accuracy of the SDS estimation method and reduce the required number of GNSSs. The estimation algorithm was established based on shape superposition with various combined response data (displacement, slope, and strain) and the least-squares method. The proposed SDS estimation method was verified using a finite element method model. In the validation process, three important issues that may affect the estimation accuracy were analyzed: effect of shape function type, sensor placement method, and effectiveness of using multi-response data. Then, the improved SDS estimation method developed in this study was compared with existing SDS estimation methods from the literature. Consequently, it was found that the proposed method can reduce the number of displacement data required to estimate rational SDS by using additional slope and strain data. It is expected that cost-effective structural health monitoring (SHM) can be established using the proposed estimation method.


Author(s):  
W. A. Paciorek ◽  
M. Meyer ◽  
G. Chapuis

The geometry of a modern imaging diffractometer is discussed in detail. A method to find all relevant instrument parameters from the control single-crystal measurement data is proposed and the limitations of such a procedure are indicated. Optimization of the instrument parameters by the least-squares method is presented.


2019 ◽  
Vol 49 (3) ◽  
pp. 65-96
Author(s):  
Kamil Krasuski ◽  
Ewelina Kobiałka ◽  
Janusz Ćwiklak ◽  
Marek Grzegorzewski

Abstract The article presents the results of aircraft positioning using GPS/GLONASS data in air navigation. In the work, the flight trajectory of the Cessna 172 aircraft was determined on the basis of GPS, GLONASS and GPS/GLONASS data. The coordinates of the Cessna 172 were determined using the least squares method in a stochastic processing compliant with the ICAO recommendations. In the air test, the Cessna 172 made a test flight over EPDE military airfield in Dęblin. The GPS, GLONASS and GPS/GLONASS measurement data from the Topcon HiperPro on-board aircraft installed on the Cessna 172 aircraft were used in the research experiment. The coordinates of the Cessna 172 in the geocentric XYZ and ellipsoidal BLh were compared with the precise flight reference trajectory determined from the differential technique RTK-OTF.


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