scholarly journals INVESTIGATION OF PARAMETERS OF THE PROBLEM OF SPLINE APPROXIMATION OF NOISY DATA BY NUMERICAL METHODS OF OPTIMAL CONTROL

2021 ◽  
Vol 21 (3) ◽  
pp. 138-148
Author(s):  
I.P. Bolodurina ◽  
◽  
L.S. Grishina ◽  
L.M. Antsiferova
Keyword(s):  
Numerical Study ◽  
Spline Approximation ◽  
Measurement Data ◽  
Noisy Data ◽  
Quality Criteria ◽  
Projection Algorithm ◽  
Model Parameters ◽  
Piecewise Constant Control ◽  
Distribution Laws ◽  
Distorted Data

Currently, the problems of distortion of measurement data by noise and the appearance of un-certainties in quality criteria have caused increased interest in research in the field of spline approx-imation. At the same time, existing methods of minimizing empirical risk, assuming that the noise is a uniform distribution with heavier tails than Gaussian, limit the scope of application of these studies. The problem of estimating noise-distorted data is usually based on solving an optimi-zation problem with a function containing uncertainty arising from the problem of finding optimal parameters. In this regard, the estimation of distorted noise cannot be solved by classical methods. Aim. This study is aimed at solving and analyzing the problem of spline approximation of data under uncertainty conditions based on the parametrization of control and the gradient projec-tion algorithm. Methods. The study of the problem of spline approximation of noisy data is carried out by the method of approximation of the piecewise constant control function. In this case, para-metrization of the control is possible only for a finite number of break points of the first kind. In the framework of the experimental study, the gradient projection algorithm is used for the numerical solution of the spline approximation problem. The proposed methods are used to study the parameters of the problem of spline approximation of data under conditions of uncertain-ty. Results. The numerical study of the control parametrization approach and the gradient projec-tion algorithm is based on the developed software and algorithmic tool for solving the problem of the spline approximation model under uncertainty. To evaluate the noise-distorted data, numerical experiments were conducted to study the model parameters and it was found that increasing the value of the parameter α leads to an increase in accuracy, but a loss of smoothness. In addition, the analysis showed that the considered distribution laws did not change the accuracy and convergence rate of the algorithm. Conclusion. The proposed approach for solving the problem of spline approx-imation under uncertainty conditions allows us to determine the problems of distortion of measure-ment data by noise and the appearance of uncertainties in the quality criteria. The study of the model parameters showed that the constructed system is stable to the error of the initial approxima-tion, and the distribution laws do not significantly affect the accuracy and convergence of the gra-dient projection method.

scholarly journals Modeling of German Low Voltage Cables with Ground Return Path

Energies ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1265 ◽  
Author(s):  
Johanna Geis-Schroer ◽  
Sebastian Hubschneider ◽  
Lukas Held ◽  
Frederik Gielnik ◽  
Michael Armbruster ◽  
...  
Keyword(s):  
Low Voltage ◽  
Measurement Data ◽  
Analytical Calculation ◽  
Laboratory Measurement ◽  
Model Parameters ◽  
Calculation Methods ◽  
Modeling Approach ◽  
Measurement Results ◽  
Simulation Results ◽  
Return Path

In this contribution, measurement data of phase, neutral, and ground currents from real low voltage (LV) feeders in Germany is presented and analyzed. The data obtained is used to review and evaluate common modeling approaches for LV systems. An alternative modeling approach for detailed cable and ground modeling, which allows for the consideration of typical German LV earthing conditions and asymmetrical cable design, is proposed. Further, analytical calculation methods for model parameters are described and compared to laboratory measurement results of real LV cables. The models are then evaluated in terms of parameter sensitivity and parameter relevance, focusing on the influence of conventionally performed simplifications, such as neglecting house junction cables, shunt admittances, or temperature dependencies. By comparing measurement data from a real LV feeder to simulation results, the proposed modeling approach is validated.

A Numerical Study of Sensitivity Coefficients for a Model of Amyloid Precursor Protein and Tubulin-Associated Unit Protein Transport and Agglomeration in Neurons at the Onset of Alzheimer's Disease

2019 ◽  
Vol 141 (3) ◽  
Author(s):  
I. A. Kuznetsov ◽  
A. V. Kuznetsov
Keyword(s):  
Alzheimer’S Disease ◽  
Alzheimer's Disease ◽  
Amyloid Precursor Protein ◽  
Tau Protein ◽  
Protein Transport ◽  
Numerical Study ◽  
Amyloid Β ◽  
Precursor Protein ◽  
Model Parameters ◽  
In The Beginning

Modeling of intracellular processes occurring during the development of Alzheimer's disease (AD) can be instrumental in understanding the disease and can potentially contribute to finding treatments for the disease. The model of intracellular processes in AD, which we previously developed, contains a large number of parameters. To distinguish between more important and less important parameters, we performed a local sensitivity analysis of this model around the values of parameters that give the best fit with published experimental results. We show that the influence of model parameters on the total concentrations of amyloid precursor protein (APP) and tubulin-associated unit (tau) protein in the axon is reciprocal to the influence of the same parameters on the average velocities of the same proteins during their transport in the axon. The results of our analysis also suggest that in the beginning of AD the aggregation of amyloid-β and misfolded tau protein have little effect on transport of APP and tau in the axon, which suggests that early damage in AD may be reversible.

Dynamic Data-Driven Spatiotemporal System Behavior Prediction With Simulations and Sensor Measurement Data

2018 ◽  
Author(s):  
Xiangxue Zhao ◽  
Shapour Azarm ◽  
Balakumar Balachandran
Keyword(s):  
Dynamical System ◽  
Real Time ◽  
Measurement Data ◽  
Data Driven ◽  
Sensor Data ◽  
Model Parameters ◽  
High Fidelity ◽  
System Behavior ◽  
Sensor Measurement

Online prediction of dynamical system behavior based on a combination of simulation data and sensor measurement data has numerous applications. Examples include predicting safe flight configurations, forecasting storms and wildfire spread, estimating railway track and pipeline health conditions. In such applications, high-fidelity simulations may be used to accurately predict a system’s dynamical behavior offline (“non-real time”). However, due to the computational expense, these simulations have limited usage for online (“real-time”) prediction of a system’s behavior. To remedy this, one possible approach is to allocate a significant portion of the computational effort to obtain data through offline simulations. The obtained offline data can then be combined with online sensor measurements for online estimation of the system’s behavior with comparable accuracy as the off-line, high-fidelity simulation. The main contribution of this paper is in the construction of a fast data-driven spatiotemporal prediction framework that can be used to estimate general parametric dynamical system behavior. This is achieved through three steps. First, high-order singular value decomposition is applied to map high-dimensional offline simulation datasets into a subspace. Second, Gaussian processes are constructed to approximate model parameters in the subspace. Finally, reduced-order particle filtering is used to assimilate sparsely located sensor data to further improve the prediction. The effectiveness of the proposed approach is demonstrated through a case study. In this case study, aeroelastic response data obtained for an aircraft through simulations is integrated with measurement data obtained from a few sparsely located sensors. Through this case study, the authors show that along with dynamic enhancement of the state estimates, one can also realize a reduction in uncertainty of the estimates.

scholarly journals Dynamic torque calibration by means of model parameter identification

ACTA IMEKO ◽  
2015 ◽  
Vol 4 (2) ◽  
pp. 39 ◽  
Author(s):  
Leonard Klaus ◽  
Barbora Arendacká ◽  
Michael Kobusch ◽  
Thomas Bruns
Keyword(s):  
Frequency Response ◽  
Dynamic Behaviour ◽  
Measurement Data ◽  
Model Parameters ◽  
Dynamic Calibration ◽  
Extended Model ◽  
Unknown Parameters ◽  
Measuring Device ◽  
Torque Transducer ◽  
Least Squares Approach

For the dynamic calibration of torque transducers, a model of the transducer and an extended model of the mounted transducer including the measuring device have been developed. The dynamic behaviour of a torque transducer under test is going to be described by its model parameters. This paper describes the models with these known and unknown parameters and how the calibration measurements are going to be carried out. The principle for the identification of the transducer's model parameters from measurement data is described using a least squares approach. The influence of a variation of the transducer's parameters on the frequency response of the expanded model is analysed.

Can high-frequency data enable better parameterization of water quality models and disentangling of DO processes?

2021 ◽  
Author(s):  
Jingshui Huang ◽  
Pablo Merchan-Rivera ◽  
Gabriele Chiogna ◽  
Markus Disse ◽  
Michael Rode
Keyword(s):  
Water Quality ◽  
High Frequency ◽  
Critical Role ◽  
Measurement Data ◽  
High Frequency Data ◽  
Model Parameters ◽  
Frequency Data ◽  
Quality Models ◽  
Model Parameter ◽  
Water Quality Models

<p>Water quality models offer to study dissolved oxygen (DO) dynamics and resulting DO balances. However, the infrequent temporal resolution of measurement data commonly limits the reliability of disentangling and quantifying instream DO process fluxes using models. These limitations of the temporal data resolution can result in the equifinality of model parameter sets. In this study, we aim to quantify the effect of the combination of emerging high-frequency monitoring techniques and water quality modelling for 1) improving the estimation of the model parameters and 2) reducing the forward uncertainty of the continuous quantification of instream DO balance pathways.</p><p>To this end, synthetic measurements for calibration with a given series of frequencies are used to estimate the model parameters of a conceptual water quality model of an agricultural river in Germany. The frequencies vary from the 15-min interval, daily, weekly, to monthly. A Bayesian inference approach using the DREAM algorithm is adopted to perform the uncertainty analysis of DO simulation. Furthermore, the propagated uncertainties in daily fluxes of different DO processes, including reaeration, phytoplankton metabolism, benthic algae metabolism, nitrification, and organic matter deoxygenation, are quantified.</p><p>We hypothesize that the uncertainty will be larger when the measurement frequency of calibrated data was limited. We also expect that the high-frequency measurements significantly reduce the uncertainty of flux estimations of different DO balance components. This study highlights the critical role of high-frequency data supporting model parameter estimation and its significant value in disentangling DO processes.</p>

Numerical study of Zika model as a mosquito-borne virus with non-singular fractional derivative

2021 ◽  
Author(s):  
Sachin Kumar ◽  
Dia Zeidan
Keyword(s):  
Fractional Derivative ◽  
Zika Virus ◽  
Numerical Study ◽  
Asymptomatic Carrier ◽  
Virus Transmission ◽  
Model Parameters ◽  
Human Society ◽  
Sexual Interaction ◽  
Virus Model ◽  
Global Threat

Zika virus infection, which is closely related to dengue, is becoming a global threat to human society. The transmission of the Zika virus from one human to another is spread by bites of Aedes mosquitoes. Recent studies also reveal the fact that the Zika virus can be transmitted by sexual interaction. In this paper, we use the fractional derivative with Mittag–Leffler non-singular kernel to study Zika virus transmission dynamics. This fractional is also known as the Atangana–Baleanu Caputo (ABC) derivative which is employed for the resulting system of ordinary differential equations. We investigate the proposed Zika virus model by using the Legendre spectral method. The model parameters are estimated and validated numerically by investigating the effect of fractional order exponent on various cases such as Susceptible human, infected human, asymptomatic carrier, exposed human, and recovered human. Numerical results obtained with the proposed method have been compared with exact solutions, showing in all parameters a very satisfactory agreement.

Numerical Study of Rotor–Stator Interaction of a Centrifugal Pump at Part Load With Special Emphasis on Unsteady Blade Load

2020 ◽  
Vol 142 (8) ◽  
Author(s):  
Nicolas Casimir ◽  
Xiangyuan Zhu ◽  
Markus Hundshagen ◽  
Gerhard Ludwig ◽  
Romuald Skoda
Keyword(s):  
Flow Field ◽  
Unsteady Flow ◽  
Centrifugal Pump ◽  
Numerical Study ◽  
Measurement Data ◽  
Load Flow ◽  
Secondary Outcome ◽  
Pump Design ◽  
Part Load ◽  
Unsteady Characteristics

Abstract Three-dimensional (3D) unsteady Reynolds-averaged Navier–Stokes (URANS) flow simulations are conducted to investigate the highly unsteady flow field at part load operation of a centrifugal pump. By the availability of unsteady flow field measurement data in the impeller wake region, a thorough validation of the simulation method is performed. Grid independence of the results is ensured. Unsteady characteristics in terms of head and shaft power as well as transient blade loads are evaluated to assess the unsteady pump performance. Significant mis-loading of the blading is revealed when one blade passes the volute tongue and associated with the strong unsteady and 3D flow field in the impeller-volute tongue region. Negative radial velocity in the tongue region is the origin of a vortex at the blade pressure side and a subsequent pressure drop that leads to even temporally negative blade loading. The results provide a detailed insight in the complex part load flow field that might be utilized for an improved pump design. As a valuable secondary outcome, a comparison of results obtained by two widely used computational fluid dynamics (CFD) codes for pump flow simulation is provided, i.e., the commercial code ansyscfx and the branch foam-extend of the open source software openfoam. It is found that the results of both methods in terms of unsteady characteristics as well as local ensemble-averaged velocity field are consistent.

Development of High Speed and High Temperature Atomic Layer Thermopiles

2019 ◽  
Author(s):  
Lakshya Bhatnagar ◽  
Guillermo Paniagua
Keyword(s):  
Heat Flux ◽  
High Temperature ◽  
High Speed ◽  
Cooling System ◽  
Numerical Study ◽  
Measurement Data ◽  
Atomic Layer ◽  
Heat Fluxes ◽  
Heat Transfer Analysis ◽  
Uncertainty Estimates

Abstract This work aims to provide a technique with which high frequency heat flux measurement data can be acquired in systems with high operational temperatures and high-speed flows with quantifiable and accurate uncertainty estimates. This manuscript presents the detailed calibration and application of an atomic layer thermopile, for heat fluxes with a frequency bandwidth of 0 to 1MHz. Two calibration procedures with a detailed uncertainty analysis. The first procedure consists using a laser to deliver radiation heat flux, while the second consists of a convective heat blowdown experiment. The use of this probe is demonstrated in a high-speed environment at Mach 2. The sensor effectively captures the passage of the normal shock wave and the values are compared with those computed using surface temperature measurement. Finally, a numerical study is carried out to design a cooling system that will allow the sensor to survive in high temperature conditions of 1273K while the sensor film is maintained at 323K. A two-dimensional axisymmetric conjugate heat transfer analysis is carried out to obtain the desired geometry.

A Sensitivity Study of the Porcine Head Subjected to Bump Impact

2016 ◽  
Author(s):  
Kimberly A. Thompson ◽  
Adam C. Sokolow ◽  
Juliana Ivancik ◽  
Timothy G. Zhang ◽  
William H. Mermagen ◽  
...  
Keyword(s):  
Human Brain ◽  
3D Model ◽  
Porcine Model ◽  
Load Transfer ◽  
Numerical Study ◽  
Sensitivity Study ◽  
Complex Problem ◽  
Model Parameters ◽  
Skin Thickness ◽  
The Impact

Understanding load transfer to the human brain is a complex problem that has been a key subject of recent investigations [4–6]. Because the porcine is a gyrencephalic species, having greater structural and functional similarities to the human brain than other lower species outlined in the literature, it is commonly chosen as a surrogate for human brain studies [7]. Consequently, we have chosen to use a porcine model in this work. To understand stress wave transfer to and through the brain, it is important to fully characterize the nature of the impact (i.e. source, location, and speed) as well as the response of the constituent tissues under such impact. We suspect the material and topology of these tissues play an important role in their response. In this paper, we report on a numerical study assessing the sensitivity of model parameters for a 6-month old Gottingen mini-pig model, under bump loading. In this study, 2D models are used for computational simplicity. While a 3D model is more realistic in nature, a 2D representation is still valuable in that it can provide trends on parameter sensitivity that can help steer the development of the 3D model. In this work, we investigate the variation of skull and skin thickness, evaluate material variability of the skull, and consider the effects of nasal cavities on load transfer. Eighty simulations are computed in LS-DYNA and analyzed in MATLAB. The results of this study will provide useful knowledge on the necessary components and parameters of the porcine model and therefore provide more confidence in the analysis. This is an essential first step as we look toward bridging the gap between correlates of injury in animal and human models.

Numerical Study on Circulation and Thermohaline Structures With Effects of Icing Event in the Caspian Sea

2010 ◽  
Author(s):  
Daisuke Kitazawa ◽  
Jing Yang
Keyword(s):  
Numerical Simulation ◽  
Water Temperature ◽  
Coriolis Force ◽  
Caspian Sea ◽  
Numerical Study ◽  
Measurement Data ◽  
Ocean Model ◽  
Water Current ◽  
The Caspian Sea ◽  
Volga River

A hydrostatic and ice coupled model was developed to analyze circulation and thermohaline structures in the Caspian Sea. The northern part of the Caspian Sea freezes in the winter. Waters start icing in November and ices spread during December and January. The northern part of the Caspian Sea is covered by ices in severe winters. Ice-covered area is at its maximum during January and February, and then ices begin melting in March and disappear in April. The occurrence of ices must have significant effects on circulation and thermohaline structures as well as ecosystem in the northern Caspian Sea. In the present study, formation of ices is modeled assuming that ices do not move but spread and shrink on water surface. Under the ices, it is assumed that the exchange of momentum flux is impeded and the fluxes of heat and brine salt are given at sea-ice boundary. The ice model was coupled with a hydrostatic model based on MEC (Marine Environmental Committee) Ocean Model developed by the Japan Society of Naval Architect and Ocean Engineers. Numerical simulation was carried out for 20 years to achieve stable seasonal changes in current velocity, water temperature, and salinity. The fluxes of momentum, heat, and salt were estimated by using measurement data at 11 meteorological stations around the Caspian Sea. Inflow of Volga River was taken into account as representative of all the rivers which inflow into the Caspian Sea. Effects of icing event on circulation and thermohaline structures were discussed using the results of numerical simulation in the last year. As a result, the accuracy of predicting water temperature in the northern Caspian Sea was improved by taking the effects of icing event into account. Differences in density in the horizontal direction create several gyres with the effects of Coriolis force. The differences were caused by differences in heat capacity between coastal and open waters, differences in water temperature due to climate, and inflow of rivers in the northern Caspian Sea. The water current field in the Caspian Sea is formed by adding wind-driven current to the dominant density-driven current, which is based on horizontal differences in water temperature and salinity, and Coriolis force.

Sign in / Sign up

Export Citation Format

Share Document