scholarly journals A review of benchmark experiments for the validation of peridynamics models

2021 ◽  
Author(s):  
Patrick Diehl
Keyword(s):  
Imaging Techniques ◽  
A Priori ◽  
Model Parameters ◽  
Length Scale ◽  
Numerical Techniques ◽  
Displacement Fields ◽  
Non Local ◽  
Simulation Results ◽  
Discontinuous Displacement ◽  
Local Nature

Peridynamics (PD), a non-local generalization of classical continuum mechanics (CCM) allowing for discontinuous displacement fields, provides an attractive framework for the modeling and simulation of fracture mechanics applications. However, PD introduces new model parameters, such as the so-called horizon parameter. The length scale of the horizon is a priori unknown and need to be identified. Moreover, the treatment of the boundary conditions is also problematic due to the non-local nature of PD models. It has thus become crucial to calibrate the new PD parameters and assess the model adequacy based on experimental observations. The objective of the present paper is to review and catalog available experimental set-ups that have been used to date for the calibration and validation of peridynamics. We have identified and analyzed a total of 39 publications that compare PD-based simulation results with experimental data. In particular, we have systematically reported, whenever possible, either the relative error or the R-squared coefficient. The best correlations were obtained in the case of experiments involving aluminum and steel materials. Experiments based on imaging techniques were also considered. However, images provide large amounts of information and their comparison with simulations is in that case far from trivial. A total of 6 publications have been identified and summarized, that introduce numerical techniques for extracting additional attributes from peridynamics simulations in order to facilitate the comparison against image-based data.

scholarly journals Tempered fractional LES modeling

2021 ◽  
Vol 932 ◽  
Author(s):  
Mehdi Samiee ◽  
Ali Akhavan-Safaei ◽  
Mohsen Zayernouri
Keyword(s):  
Isotropic Turbulence ◽  
Stokes Equations ◽  
A Priori ◽  
Correlation Coefficients ◽  
Scale Model ◽  
Navier Stokes ◽  
Model Parameters ◽  
Subgrid Scale ◽  
Modelling Framework ◽  
Non Local

The presence of non-local interactions and intermittent signals in the homogeneous isotropic turbulence grant multi-point statistical functions a key role in formulating a new generation of large-eddy simulation (LES) models of higher fidelity. We establish a tempered fractional-order modelling framework for developing non-local LES subgrid-scale models, starting from the kinetic transport. We employ a tempered Lévy-stable distribution to represent the source of turbulent effects at the kinetic level, and we rigorously show that the corresponding turbulence closure term emerges as the tempered fractional Laplacian, $(\varDelta +\lambda )^{\alpha } (\cdot )$ , for $\alpha \in (0,1)$ , $\alpha \neq \frac {1}{2}$ and $\lambda >0$ in the filtered Navier–Stokes equations. Moreover, we prove the frame invariant properties of the proposed model, complying with the subgrid-scale stresses. To characterize the optimum values of model parameters and infer the enhanced efficiency of the tempered fractional subgrid-scale model, we develop a robust algorithm, involving two-point structure functions and conventional correlation coefficients. In an a priori statistical study, we evaluate the capabilities of the developed model in fulfilling the closed essential requirements, obtained for a weaker sense of the ideal LES model (Meneveau, Phys. Fluids, vol. 6, issue 2, 1994, pp. 815–833). Finally, the model undergoes the a posteriori analysis to ensure the numerical stability and pragmatic efficiency of the model.

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.

Generalised DOPs with Consideration of the Influence Function of Signal-in-Space Errors

2011 ◽  
Vol 64 (S1) ◽  
pp. S3-S18 ◽  
Author(s):  
Yuanxi Yang ◽  
Jinlong Li ◽  
Junyi Xu ◽  
Jing Tang
Keyword(s):  
Least Squares ◽  
Stochastic Models ◽  
Influence Function ◽  
A Priori ◽  
Functional Model ◽  
Global Navigation Satellite Systems ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Integrated Navigation ◽  
Satellite Systems

Integrated navigation using multiple Global Navigation Satellite Systems (GNSS) is beneficial to increase the number of observable satellites, alleviate the effects of systematic errors and improve the accuracy of positioning, navigation and timing (PNT). When multiple constellations and multiple frequency measurements are employed, the functional and stochastic models as well as the estimation principle for PNT may be different. Therefore, the commonly used definition of “dilution of precision (DOP)” based on the least squares (LS) estimation and unified functional and stochastic models will be not applicable anymore. In this paper, three types of generalised DOPs are defined. The first type of generalised DOP is based on the error influence function (IF) of pseudo-ranges that reflects the geometry strength of the measurements, error magnitude and the estimation risk criteria. When the least squares estimation is used, the first type of generalised DOP is identical to the one commonly used. In order to define the first type of generalised DOP, an IF of signal–in-space (SIS) errors on the parameter estimates of PNT is derived. The second type of generalised DOP is defined based on the functional model with additional systematic parameters induced by the compatibility and interoperability problems among different GNSS systems. The third type of generalised DOP is defined based on Bayesian estimation in which the a priori information of the model parameters is taken into account. This is suitable for evaluating the precision of kinematic positioning or navigation. Different types of generalised DOPs are suitable for different PNT scenarios and an example for the calculation of these DOPs for multi-GNSS systems including GPS, GLONASS, Compass and Galileo is given. New observation equations of Compass and GLONASS that may contain additional parameters for interoperability are specifically investigated. It shows that if the interoperability of multi-GNSS is not fulfilled, the increased number of satellites will not significantly reduce the generalised DOP value. Furthermore, the outlying measurements will not change the original DOP, but will change the first type of generalised DOP which includes a robust error IF. A priori information of the model parameters will also reduce the DOP.

scholarly journals De Sitter and power-law solutions in non-local Gauss–Bonnet gravity

2018 ◽  
Vol 15 (11) ◽  
pp. 1850188 ◽  
Author(s):  
E. Elizalde ◽  
S. D. Odintsov ◽  
E. O. Pozdeeva ◽  
S. Yu. Vernov
Keyword(s):  
Power Law ◽  
Sufficient Conditions ◽  
Model Parameters ◽  
Local Form ◽  
De Sitter ◽  
Dynamical Equations ◽  
Non Local ◽  
Necessary And Sufficient ◽  
The Universe ◽  
Universe Evolution

The cosmological dynamics of a non-locally corrected gravity theory, involving a power of the inverse d’Alembertian, is investigated. Casting the dynamical equations into local form, the fixed points of the models are derived, as well as corresponding de Sitter and power-law solutions. Necessary and sufficient conditions on the model parameters for the existence of de Sitter solutions are obtained. The possible existence of power-law solutions is investigated, and it is proven that models with de Sitter solutions have no power-law solutions. A model is found, which allows to describe the matter-dominated phase of the Universe evolution.

scholarly journals Bond-Length Distributions for Ions Bonded to Oxygen: Results for the Transition Metals and Quantification of the Factors Underlying Bond-Length Variation in Inorganic Solids

2020 ◽  
Author(s):  
Olivier Charles Gagné ◽  
Frank Christopher Hawthorne
Keyword(s):  
Transition Metal ◽  
Bond Length ◽  
A Priori ◽  
Bond Formation ◽  
Length Variation ◽  
Electronic Effects ◽  
Coordination Polyhedra ◽  
Jahn Teller ◽  
Jahn Teller Effect ◽  
Non Local

Bond-length distributions are examined for 63 transition-metal ions bonded to O2- in 147 configurations, for 7522 coordination polyhedra and 41,488 bond distances, providing baseline statistical knowledge of bond lengths for transi-tion metals bonded to O2-. A priori bond valences are calculated for 140 crystal structures containing 266 coordination poly-hedra for 85 transition-metal ion configurations with anomalous bond-length distributions. Two new indices, Δ𝑡𝑜𝑝𝑜𝑙 and Δ𝑐𝑟𝑦𝑠𝑡, are proposed to quantify bond-length variation arising from bond-topological and crystallographic effects in extended solids. Bond-topological mechanisms of bond-length variation are [1] non-local bond-topological asymmetry, and [2] multi-ple-bond formation; crystallographic mechanisms are [3] electronic effects (with inherent focus on coupled electronic-vibra-tional degeneracy in this work), and [4] crystal-structure effects. The Δ𝑡𝑜𝑝𝑜𝑙 and Δ𝑐𝑟𝑦𝑠𝑡 indices allow one to determine the primary cause(s) of bond-length variation for individual coordination polyhedra and ion configurations, quantify the dis-torting power of cations via electronic effects (by subtracting the bond-topological contribution to bond-length variation), set expectation limits regarding the extent to which functional properties linked to bond-length variations may be optimized in a given crystal structure (and inform how optimization may be achieved), and more. We find the observation of multiple bonds to be primarily driven by the bond-topological requirements of crystal structures in solids. However, we sometimes observe multiple bonds to form as a result of electronic effects (e.g. the pseudo Jahn-Teller effect); resolution of the origins of multiple-bond formation follows calculation of the Δ𝑡𝑜𝑝𝑜𝑙 and Δ𝑐𝑟𝑦𝑠𝑡 indices on a structure-by-structure basis. Non-local bond-topological asymmetry is the most common cause of bond-length variation in transition-metal oxides and oxysalts, followed closely by the pseudo Jahn-Teller effect (PJTE). Non-local bond-topological asymmetry is further suggested to be the most widespread cause of bond-length variation in the solid state, with no a priori limitations with regard to ion identity. Overall, bond-length variations resulting from the PJTE are slightly larger than those resulting from non-local bond-topological asym-metry, comparable to those resulting from the strong JTE, and less than those induced by π-bond formation. From a compar-ison of a priori and observed bond valences for ~150 coordination polyhedra in which the strong JTE or the PJTE is the main reason underlying bond-length variation, the Jahn-Teller effect is found not to have a symbiotic relation with the bond-topo-logical requirements of crystal structures. The magnitude of bond-length variations caused by the PJTE decreases in the fol-lowing order for octahedrally coordinated d0 transition metals oxyanions: Os8+ > Mo6+ > W6+ >> V5+ > Nb5+ > Ti4+ > Ta5+ > Hf4+ > Zr4+ > Re7+ >> Y3+ > Sc3+. Such ranking varies by coordination number; for [4], it is Re7+ > Ti4+ > V5+ > W6+ > Mo6+ > Cr6+ > Os8+ >> Mn7+; for [5], it is Os8+ > Re7+ > Mo6+ > Ti4+ > W6+ > V5+ > Nb5+. We conclude that non-octahedral coordinations of d0 ion configurations are likely to occur with bond-length variations that are similar in magnitude to their octahedral counterparts. However, smaller bond-length variations are expected from the PJTE for non-d0 transition-metal oxyanions.<br>

scholarly journals Technology of Quick-Frozen Flour Fish Culinary Products

2022 ◽  
Author(s):  
Valentina Pavlova ◽  
Irina Saenkova ◽  
Yulia Shokina ◽  
Grigoriy Shokin
Keyword(s):  
Mass Fraction ◽  
High Efficiency ◽  
A Priori ◽  
Cholesterol Content ◽  
Organoleptic Evaluation ◽  
Amine Nitrogen ◽  
Long Term Storage ◽  
Functional Product ◽  
Simulation Results ◽  
Priori Information

In this article, the results of the development of the functional fish culinary product “Thorny Skate and Cod Pie” are presented. A traditional recipe was used for making the yeast dough for the pie. The pie filling recipe was designed using Fuzzy Logic in the Matlab software package.Optimized parametersfor the selected sensory evaluation of the pie were calculated. On the basis of a priori information, key components of the filling (including the fraction of the fish components and skate meat) were chosen as the factors of interest. According to the simulation results, the optimal values werea 50/50 percentage for the first and the second factor respectively, and this providedthe maximum organoleptic assessment (five points on a five-point scale). The simulation results were compared with the results of the organoleptic evaluation of the pie made according to the optimized recipe, and their sufficient convergence was shown. The indicators of mass fraction of amine nitrogen and nitrogen of volatile bases was studied, as well as the microbiological safety indicators of flour fish culinary products, in accordance with the requirements of the Technical Regulations of the Eurasian Economic Union 040/2016 ”On the safety of fish products”. The results showed a high efficiency of the shock freezing of the semi-finished product, brought to semi-readiness, for long-term storage (120 days at a temperature no higher than minus 18 ∘C), without reducing the quality or safety of the pie. The product had a cholesterol content from 220 to 260 mg%, which allowed it to be classified as functional. The nutritional values of the product (mass fraction of protein, fat, carbohydrates, and amino acid composition) are presented. Keywords: thornyskate, functional product, pie with thornyskate and cod, shock freezing

scholarly journals Technical Note: Improved sampling of behavioral subsurface flow model parameters using active subspaces

2020 ◽  
Vol 24 (9) ◽  
pp. 4567-4574
Author(s):  
Daniel Erdal ◽  
Olaf A. Cirpka
Keyword(s):  
A Priori ◽  
Behavioral Model ◽  
Technical Note ◽  
Sampling Scheme ◽  
Model Parameters ◽  
Test Case ◽  
Sampling Efficiency ◽  
Subspace Decomposition ◽  
Plausible Model ◽  
Active Subspaces

Abstract. In global sensitivity analysis and ensemble-based model calibration, it is essential to create a large enough sample of model simulations with different parameters that all yield plausible model results. This can be difficult if a priori plausible parameter combinations frequently yield non-behavioral model results. In a previous study (Erdal and Cirpka, 2019), we developed and tested a parameter-sampling scheme based on active-subspace decomposition. While in principle this scheme worked well, it still implied testing a substantial fraction of parameter combinations that ultimately had to be discarded because of implausible model results. This technical note presents an improved sampling scheme and illustrates its simplicity and efficiency by a small test case. The new sampling scheme can be tuned to either outperform the original implementation by improving the sampling efficiency while maintaining the accuracy of the result or by improving the accuracy of the result while maintaining the sampling efficiency.

scholarly journals ONLINE PARAMETER IDENTIFICATION OF RICE TRANSPLANTER MODEL BASED ON IPSO-EKF ALGORITHM

2020 ◽  
Vol 61 (2) ◽  
pp. 25-34 ◽  
Author(s):  
Yibo Li ◽  
Hang Li ◽  
Xiaonan Guo
Keyword(s):  
Parameter Identification ◽  
Measured Data ◽  
Model Parameters ◽  
Identification Algorithm ◽  
Output Data ◽  
Swarm Optimization ◽  
Model Based ◽  
Simulation Results ◽  
Filtering Effect ◽  
Ipso Algorithm

In order to improve the accuracy of rice transplanter model parameters, an online parameter identification algorithm for the rice transplanter model based on improved particle swarm optimization (IPSO) algorithm and extended Kalman filter (EKF) algorithm was proposed. The dynamic model of the rice transplanter was established to determine the model parameters of the rice transplanter. Aiming at the problem that the noise matrices in EKF algorithm were difficult to select and affected the best filtering effect, the proposed algorithm used the IPSO algorithm to optimize the noise matrices of the EKF algorithm in offline state. According to the actual vehicle tests, the IPSO-EKF was used to identify the cornering stiffness of the front and rear tires online, and the identified cornering stiffness value was substituted into the model to calculate the output data and was compared with the measured data. The simulation results showed that the accuracy of parameter identification for the rice transplanter model based on the IPSO-EKF algorithm was improved, and established an accurate rice transplanter model.

Modeling of a spiral-wound module and estimation of model parameters using numerical techniques

Desalination ◽  
2005 ◽  
Vol 173 (3) ◽  
pp. 269-286 ◽  
Author(s):  
S. Senthilmurugan ◽  
Aruj Ahluwalia ◽  
Sharad K. Gupta
Keyword(s):  
Model Parameters ◽  
Numerical Techniques ◽  
Estimation Of Model Parameters ◽  
Spiral Wound

Inversion and uncertainty estimation of gravity data using simulated annealing: An application over Lake Vostok, East Antarctica

Geophysics ◽  
2005 ◽  
Vol 70 (1) ◽  
pp. J1-J12 ◽  
Author(s):  
Lopamudra Roy ◽  
Mrinal K. Sen ◽  
Donald D. Blankenship ◽  
Paul L. Stoffa ◽  
Thomas G. Richter
Keyword(s):  
Simulated Annealing ◽  
Gravity Data ◽  
A Priori ◽  
Model Space ◽  
Uncertainty Estimation ◽  
East Antarctica ◽  
Airborne Gravity ◽  
Model Parameters ◽  
Data Set ◽  
Lake Vostok

Interpretation of gravity data warrants uncertainty estimation because of its inherent nonuniqueness. Although the uncertainties in model parameters cannot be completely reduced, they can aid in the meaningful interpretation of results. Here we have employed a simulated annealing (SA)–based technique in the inversion of gravity data to derive multilayered earth models consisting of two and three dimensional bodies. In our approach, we assume that the density contrast is known, and we solve for the coordinates or shapes of the causative bodies, resulting in a nonlinear inverse problem. We attempt to sample the model space extensively so as to estimate several equally likely models. We then use all the models sampled by SA to construct an approximate, marginal posterior probability density function (PPD) in model space and several orders of moments. The correlation matrix clearly shows the interdependence of different model parameters and the corresponding trade-offs. Such correlation plots are used to study the effect of a priori information in reducing the uncertainty in the solutions. We also investigate the use of derivative information to obtain better depth resolution and to reduce underlying uncertainties. We applied the technique on two synthetic data sets and an airborne-gravity data set collected over Lake Vostok, East Antarctica, for which a priori constraints were derived from available seismic and radar profiles. The inversion results produced depths of the lake in the survey area along with the thickness of sediments. The resulting uncertainties are interpreted in terms of the experimental geometry and data error.

Sign in / Sign up

Export Citation Format

Share Document